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  137.Thefollowingtableshowsthenumberofstudentsinthreedifferentdegreeprogramsandwhethertheyaregraduateorundergraduatestudents:         Undergraduate Graduate Total Business 150 50 200 Engineering 150 25 175 Arts&Sciences 100 25 125 Total 400 100 500     a.Whatistheprobabilitythatarandomlyselectedstudentisanundergraduate? b.Whatpercentageofstudentsisengineeringmajors? c.Ifweknowthataselectedstudentisanundergraduate,whatistheprobabilitythatheorsheisabusinessmajor? d.AstudentisenrolledintheArtsandSciencesschool.Whatistheprobabilitythatthestudentisanundergraduatestudent? e.WhatistheprobabilitythatarandomlyselectedstudentisagraduateBusinessmajor?   138.AsurveyofbusinessstudentswhohadtakentheGraduateManagementAdmissionTest(GMAT)indicatedthatstudentswhohavespentatleastfivehoursstudyingGMATreviewguideshaveaprobabilityof0.85ofscoringabove400.Studentswhodonotreviewhaveaprobabilityof0.65ofscoringabove400.Ithasbeendeterminedthat70%ofthebusinessstudentsreviewforthetest.   a.Findtheprobabilityofscoringabove400. b.Findtheprobabilitythatastudentwhoscoredabove400reviewedforthetest.     139.Amachineisusedinaproductionprocess.Frompastdata,itisknownthat97%ofthetimethemachineissetupcorrectly.Furthermore,itisknownthatifthemachineissetupcorrectly,itproduces95%acceptable(non-defective)items.However,whenitissetupincorrectly,itproducesonly40%acceptableitems.     a.Anitemfromtheproductionlineisselected.Whatistheprobabilitythattheselecteditemisnon-defective? b.Giventhattheselecteditemisnon-defective,whatistheprobabilitythatthemachineissetupcorrectly?     140.Acommitteeof4istobeselectedfromagroupof12people.Howmanypossiblecommitteescanbeselected?   141.Assumeabusinessmanhas7suitsand8ties.Heisplanningtotake3suitsand2tieswithhimonhisnextbusinesstrip.Howmanypossibilitiesofselectiondoeshehave?     142.Theresultsofasurveyof800marriedcouplesandthenumberofchildrentheyhadisshownbelow.     NumberofChildren Probability 0 0.050 1 0.125 2 0.600 3 0.150 4 0.050 5 0.025   Ifacoupleisselectedatrandom,whatistheprobabilitythatthecouplewillhave       a.Lessthan4children? b.Morethan2children? c.Either2or3children?     143.Assumethatinyourhandyouholdanordinarysix-sideddieandadime.Youtossboththedieandthedimeonatable.   a.Whatistheprobabilitythataheadappearsonthedimeandasixonthedie? b.Whatistheprobabilitythatatailappearsonthedimeandanynumbermorethan3onthedie? c.Whatistheprobabilitythatanumberlargerthan2appearsonthedie?   144.Averyshortquizhasonemultiplechoicequestionwithfivepossiblechoices(a,b,c,d,e)andonetrueorfalsequestion.Assumeyouaretakingthequizbutdonothaveanyideawhatthecorrectansweristoeitherquestion,butyoumarkanansweranyway.   a.Whatistheprobabilitythatyouhavegiventhecorrectanswertobothquestions? b.Whatistheprobabilitythatonlyoneofthetwoanswersiscorrect? c.Whatistheprobabilitythatneitheransweriscorrect? d.Whatistheprobabilitythatonlyyouranswertothemultiplechoicequestioniscorrect? e.Whatistheprobabilitythatyouhaveonlyansweredthetrueorfalsequestioncorrectly?       .
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MultipleChoice 1.Anumericaldescriptionoftheoutcomeofanexperimentiscalleda a.descriptivestatistic b.probabilityfunction c.variance d.randomvariable       2.Arandomvariablethatcanassumeonlyafinitenumberofvaluesisreferredtoasa(n) a.infinitesequence b.finitesequence c.discreterandomvariable d.discreteprobabilityfunction     3.Aprobabilitydistributionshowingtheprobabilityofxsuccessesinntrials,wheretheprobabilityofsuccessdoesnotchangefromtrialtotrial,istermeda a.uniformprobabilitydistribution b.binomialprobabilitydistribution c.hypergeometricprobabilitydistribution d.normalprobabilitydistribution     4.Varianceis a.ameasureoftheaverage,orcentralvalueofarandomvariable b.ameasureofthedispersionofarandomvariable c.thesquarerootofthestandarddeviation d.thesumofthesquareddeviationofdataelementsfromthemean     5.Acontinuousrandomvariablemayassume a.anyvalueinanintervalorcollectionofintervals b.onlyintegervaluesinanintervalorcollectionofintervals c.onlyfractionalvaluesinanintervalorcollectionofintervals d.onlythepositiveintegervaluesinaninterval         6.Adescriptionofthedistributionofthevaluesofarandomvariableandtheirassociatedprobabilitiesiscalleda a.probabilitydistribution b.randomvariance c.randomvariable d.expectedvalue     7.Whichofthefollowingisarequiredconditionforadiscreteprobabilityfunction? a.∑f(x)=0forallvaluesofx b.f(x) 1forallvaluesofx c.f(x)<0forallvaluesofx d.∑f(x)=1forallvaluesofx     8.Ameasureoftheaveragevalueofarandomvariableiscalleda(n) a.variance b.standarddeviation c.expectedvalue d.coefficientofvariation     9.Whichofthefollowingisnotarequiredconditionforadiscreteprobabilityfunction? a.f(x)≥ 0forallvaluesofx b.∑f(x)=1forallvaluesofx c.∑f(x)=0forallvaluesofx d.∑f(x)≥ 1forallvaluesofx     10.Thestandarddeviationisthe a.variancesquared b.squarerootofthesumofthedeviationsfromthemean c.sameastheexpectedvalue d.positivesquarerootofthevariance       .
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  115.Thetimeittakestohandcarveaguitarneckisuniformlydistributedbetween110and190minutes.   a.Whatistheprobabilitythataguitarneckcanbecarvedbetween95and165minutes? b.Whatistheprobabilitythattheguitarneckcanbecarvedbetween120and200minutes? c.Determinetheexpectedcompletiontimeforcarvingtheguitarneck. d.Computethestandarddeviation.   116.Scoresonarecentnationalstatisticsexamwerenormallydistributedwithameanof80andastandarddeviationof6.   a.Whatistheprobabilitythatarandomlyselectedexamwillhaveascoreofatleast71? b.Whatpercentageofexamswillhavescoresbetween89and92? c.Ifthetop2.5%oftestscoresreceivemeritawards,whatisthelowestscoreeligibleforanaward? d.Iftherewere334examswithscoresofatleast89,howmanystudentstooktheexam?   117.Theaveragestartingsalaryofthisyear'sMBAstudentsis$35,000withastandarddeviationof$5,000.Furthermore,itisknownthatthestartingsalariesarenormallydistributed.Whataretheminimumandthemaximumstartingsalariesofthemiddle95%ofMBAgraduates?   118.Theaveragestartingsalaryforthisyear'sgraduatesatalargeuniversity(LU)is$20,000withastandarddeviationof$8,000.Furthermore,itisknownthatthestartingsalariesarenormallydistributed.     a.WhatistheprobabilitythatarandomlyselectedLUgraduatewillhaveastartingsalaryofatleast$30,400? b.Individualswithstartingsalariesoflessthan$15,600receivealowincometaxbreak.Whatpercentageofthegraduateswillreceivethetaxbreak? c.Whataretheminimumandthemaximumstartingsalariesofthemiddle95%oftheLUgraduates? d.If189oftherecentgraduateshavesalariesofatleast$32,240,howmanystudentsgraduatedthisyearfromthisuniversity?       119."DRUGSRUS"isalargemanufacturerofvariouskindsofliquidvitamins.Thequalitycontroldepartmenthasnotedthatthebottlesofvitaminsmarked6ouncesvaryincontentwithastandarddeviationof0.3ounces.Assumethecontentsofthebottlesarenormallydistributed.   a.Whatpercentageofallbottlesproducedcontainsmorethan6.51ouncesofvitamins? b.Whatpercentageofallbottlesproducedcontainslessthan5.415ounces? c.Whatpercentageofbottlesproducedcontainsbetween5.46to6.495ounces? d.Ninety-fivepercentofthebottleswillcontainatleasthowmanyounces? e.Whatpercentageofthebottlescontainsbetween6.3and6.6ounces?     .
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    21.Initialestimatesoftheprobabilitiesofeventsareknownas a.sets b.posteriorprobabilities c.conditionalprobabilities d.priorprobabilities       22.Twoeventswithnonzeroprobabilities a.canbebothmutuallyexclusiveandindependent b.cannotbebothmutuallyexclusiveandindependent c.arealwaysmutuallyexclusive d.arealwaysindependent     23.Twoevents,AandB,aremutuallyexclusiveandeachhaveanonzeroprobability.IfeventAisknowntooccur,theprobabilityoftheoccurrenceofeventBis a.one b.anypositivevalue c.zero d.anyvaluebetween0to1     24.Theadditionlawispotentiallyhelpfulwhenweareinterestedincomputingtheprobabilityof a.independentevents b.theintersectionoftwoevents c.theunionoftwoevents d.conditionalevents     25.Thesumoftheprobabilitiesoftwocomplementaryeventsis a.Zerob.0.5c.0.57d.1.0   26.EventsAandBaremutuallyexclusiveiftheirjointprobabilityis a.largerthan1 b.lessthanzero c.zero d.infinity       27.Thesetofallpossibleoutcomesofanexperimentis a.anexperiment b.anevent c.thepopulation d.thesamplespace     28.Assumingthateachofthe52cardsinanordinarydeckhasaprobabilityof1/52ofbeingdrawn,whatistheprobabilityofdrawingablackace? a.1/52b.2/52c.3/52d.4/52   29.Ifadimeistossedfourtimesandcomesuptailsallfourtimes,theprobabilityofheadsonthefifthtrialis a.smallerthantheprobabilityoftails b.largerthantheprobabilityoftailsc.1/2 d.1/32     30.If a sixsideddieistossedtwotimesand"3"showsupbothtimes,theprobabilityof"3"onthethirdtrialis a.muchlargerthananyotheroutcome b.muchsmallerthananyotheroutcomec.1/6 d.1/216       .
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    91.RefertoExhibit7-1.Thepointestimateofthemeancontentofthebottlesisa.0.22 b.4c.121 d.0.02       92.RefertoExhibit7-1.Inthisproblemthe0.22is a.aparameter b.astatistic c.thestandarderrorofthemean d.theaveragecontentofcolognesinthelongrun       Exhibit7-2 Arandomsampleof10examinationpapersinacourse,whichwasgivenonapassorfailbasis,showedthefollowingscores.       PaperNumberGradeStatus 165Pass 287Pass 392Pass 435Fail 579Pass 6100Pass 748Fail 874Pass 979Pass 1091Pass 93.RefertoExhibit7-2.Thepointestimateforthemeanofthepopulationis a.750 b.100 c.85 d.75       94.RefertoExhibit7-2.Thepointestimateforthestandarddeviationofthepopulationisa.419.43 b.20.48 c.75d.750   95.RefertoExhibit7-2.Thepointestimateforthevarianceofthepopulationisa.419.43 b.20.48 c.75d.750     96.RefertoExhibit7-2.Thepointestimatefortheproportionofallstudentswhopassedthecourseisa.0.8 b.0.2 c.1.8 d.1.2     Exhibit7-3 Inalocaluniversity,40%ofthestudentsliveinthedormitories.Arandomsampleof80studentsisselectedforaparticularstudy. 97.RefertoExhibit7-3.Thestandarddeviationof,knownasthestandarderroroftheproportionisapproximatelya.0.5477 b.5.477 c.0.05477 d.54.77       98.RefertoExhibit7-3.Theprobabilitythatthesampleproportion(theproportionlivinginthedormitories)isbetween 0.30and0.50isa.0.4664 b.0.9328 c.0.0336 d.0.0672     99.RefertoExhibit7-3.Theprobabilitythatthesampleproportion(theproportionlivinginthedormitories)isatleast 0.30is a.0.4664 b.0.9328 c.0.9664 d.0.0336             .
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  125.Thenumberofbadchecksreceivedperdaybyastoreandtherespectiveprobabilitiesareshownbelow.     NumberofBadChecksReceivedPerDay   Probability 00.04 10.06 20.10 30.30 40.20 50.15 60.10 70.05     a.Whatistheexpectednumberofbadchecksreceivedperday? b.Determinethevarianceinthenumberofbadchecksreceivedperday. c.Whatisthestandarddeviation?   126.Acosmeticssalesperson,whocallspotentialcustomerstosellherproducts,hasdeterminedthat30%ofhertelephonecallsresultinasale.Determinetheprobabilitydistributionforhernextthreecalls.Notethatthenextthreecallscouldresultin0,1,2,or3sales.     x   p 00.3430 10.4410 20.1890 30.0270 127.Thefollowingtableshowspartoftheprobabilitydistributionforarandomvariablex.       xf(x) 00.2 1? 20.15 3? 40.15       a.Themeanoftheabovedistributionisknowntobe1.8(i.e.,E(x)=1.8).Determinef(1)andf(3). b.Computethevarianceandthestandarddeviationfortheaboveprobabilitydistribution. 128.ThefollowingtableshowspartoftheprobabilitydistributionforthenumberofboatssolddailyatBoatsUnlimited.Itisknownthattheaveragenumberofboatssolddailyis1.57.     xf(x) 00.20 10.30 20.32 3? 40.05 50.02     Computethevarianceandthestandarddeviationforthisprobabilitydistribution.       .
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MultipleChoice 1.Fromagroupof12students,wewanttoselectarandomsampleof4studentstoserveonauniversitycommittee.Howmanydifferentrandomsamplesof4studentscanbeselected? a.48 b.20,736 c.16d.495     2.Parametersare a.numericalcharacteristicsofasample b.numericalcharacteristicsofapopulation c.theaveragestakenfromasample d.numericalcharacteristicsofeitherasampleorapopulation     3.Howmanysimplerandomsamplesofsize3canbeselectedfromapopulationofsize7? a.7 b.21 c.35d.343   4.Samplingdistributionofisthe a.probabilitydistributionofthesamplemean b.probabilitydistributionofthesampleproportion c.meanofthesample d.meanofthepopulation     5.Asimplerandomsampleof100observationswastakenfromalargepopulation.Thesamplemeanandthestandarddeviationweredeterminedtobe80and12respectively.Thestandarderrorofthemeanis a.1.20 b.0.12 c.8.00 d.0.80         6.Apopulationhasastandarddeviationof16.Ifasampleofsize64isselectedfromthispopulation,whatistheprobabilitythatthesamplemeanwillbewithin± 2ofthepopulationmean? a.0.6826 b.0.3413 c.-0.6826 d.Sincethemeanisnotgiven,thereisnoanswertothisquestion.     7.Theprobabilitydistributionofallpossiblevaluesofthesampleproportionisthe a.probabilitydensityfunctionof b.samplingdistributionof c.sameas,sinceitconsidersallpossiblevaluesofthesampleproportion d.samplingdistributionof   8.Incomputingthestandarderrorofthemean,thefinitepopulationcorrectionfactorisusedwhena.N/n>0.05 b.N/n≤0.05c.n/N>0.05 d.n/N≤30     9.Conveniencesamplingisanexampleof a.probabilisticsampling b.stratifiedsampling c.nonprobabilisticsampling d.clustersampling     10.Whichofthefollowingisanexampleofnonprobabilisticsampling? a.simplerandomsampling b.stratifiedsimplerandomsampling c.clustersampling d.judgmentsampling         .
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    41.Iftwoeventsareindependent,then a.theymustbemutuallyexclusive b.thesumoftheirprobabilitiesmustbeequaltoone c.theirintersectionmustbezero d.Noneofthesealternativesiscorrect.     42.Bayes'theoremisusedtocompute a.thepriorprobabilities b.theunionofevents c.intersectionofevents d.theposteriorprobabilities     43.OnaDecemberday,theprobabilityofsnowis.30.Theprobabilityofa"cold"dayis.50.Theprobabilityofsnowand"cold"weatheris.15.Aresnowand"cold"weatherindependentevents? a.onlyifgiventhatitsnowed b.no c.yes d.onlywhentheyarealsomutuallyexclusive     44.Oneofthebasicrequirementsofprobabilityis a.foreachexperimentaloutcomeEi,wemusthaveP(Ei) ≥1 b.P(A)=P(Ac)-1 c.iftherearekexperimentaloutcomes,then∑P(Ei)=1 d.∑P(Ei)≥1   45.Thesymbol∩showsthe a.unionofevents b.intersectionoftwoevents c.sumoftheprobabilitiesofevents d.samplespace   46.Thesymbol∪showsthe a.unionofevents b.intersectionoftwoevents c.sumoftheprobabilitiesofevents d.samplespace       47.Themultiplicationlawispotentiallyhelpfulwhenweareinterestedincomputingtheprobabilityof a.mutuallyexclusiveevents b.theintersectionoftwoevents c.theunionoftwoevents d.conditionalevents     48.Iftwoeventsaremutuallyexclusive,thentheirintersection a.willbeequaltozero b.canhaveanyvaluelargerthanzero c.mustbelargerthanzero,butlessthanone d.willbeone     49.TheunionofeventsAandBistheeventcontaining a.allthesamplepointsbelongingtoBorA b.allthesamplepointsbelongingtoAorB c.allthesamplepointsbelongingtoA orB orboth d.allthesamplepointsbelongingto AorB,butnotboth     50.Ifapennyistossedthreetimesandcomesupheadsallthreetimes,theprobabilityofheadsonthefourthtrialis a.zerob.1/16c.1/2 d.largerthantheprobabilityoftails       .
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    41.GiventhatZisastandardnormalrandomvariable,whatistheprobabilitythat-2.08≤Z≤1.46?a.0.9091 b.0.4812 c.0.4279 d.0.0533     42.Inastandardnormaldistributionthevalueofz a.canbeanyvalue b.cannotbenegative c.cannotbelargerthan3.09 d.cannotbelargerthan0.50       43.Zisastandardnormalrandomvariable.TheP(1.41≤Z≤ 2.85)equalsa.0.4978 b.0.4207 c.0.9185 d.0.0771     44.Xisanormallydistributedrandomvariablewithameanof8andastandarddeviationof4.TheprobabilitythatXisbetween1.48and15.56is a.0.0222 b.0.4190 c.0.5222 d.0.9190     45.Xisanormallydistributedrandomvariablewithameanof5andavarianceof4.TheprobabilitythatXisgreaterthan10.52is a.0.0029 b.0.0838 c.0.4971 d.0.9971     46.Xisanormallydistributedrandomvariablewithameanof12andastandarddeviationof3.TheprobabilitythatXequals19.62is a.0.000 b.0.0055 c.0.4945 d.0.9945     47.Xisanormallydistributedrandomvariablewithameanof22andastandarddeviationof5.TheprobabilitythatXislessthan9.7is a.0.000 b.0.4931 c.0.0069 d.0.9931         48.GiventhatZisastandardnormalrandomvariable,whatisthevalueofZiftheareatotherightofZis0.5?a.0.0000 b.1.0000 c.0.1915 d.0.3413     49.Usethenormalapproximationtothebinomialdistributiontoanswerthisquestion.FifteenpercentofallstudentsatalargeuniversityareabsentonMondays.Ifarandomsampleof12namesiscalledonaMonday,whatistheprobabilitythatfourstudentsareabsent? a.0.0683 b.0.0213 c.0.0021 d.0.1329     50.GiventhatZisastandardnormalrandomvariable,whatisthevalueofZiftheareatotheleftofZis0.0559?a.0.4441 b.1.59 c.0.0000 d.1.50       .
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  105.Therandomvariablexhasthefollowingprobabilitydistribution:     xf(x) 0.25 1.20 2.15 3.30 4.10     a.Isthisprobabilitydistributionvalid?Explainandlisttherequirementsforavalidprobabilitydistribution. b.Calculatetheexpectedvalueofx. c.Calculatethevarianceofx. d.Calculatethestandarddeviationofx.     106.TheprobabilityfunctionforthenumberofinsurancepoliciesJohnwillselltoacustomerisgivenbyf(X) = .5- (X/6)for X= 0,1,or 2 a.Isthisavalidprobabilityfunction?Explainyouranswer. b.WhatistheprobabilitythatJohnwillsellexactly2policiestoacustomer? c.WhatistheprobabilitythatJohnwillsellatleast2policiestoacustomer? d.WhatistheexpectednumberofpoliciesJohnwillsell? e.WhatisthevarianceofthenumberofpoliciesJohnwillsell?   107.Theprobabilitydistributionfortherateofreturnonaninvestmentis   RateofReturn(InPercent)   Probability 9.5.1 9.8.2 10.0.3 10.2.3 10.6.1     a.Whatistheprobabilitythattherateofreturnwillbeatleast10%? b.Whatistheexpectedrateofreturn? c.Whatisthevarianceoftherateofreturn?     108.Inalargeuniversity,75%ofstudentsliveindormitories.Arandomsampleof5studentsisselected.Usethebinomialprobabilitytablestoanswerthefollowingquestions.     a.Whatistheprobabilitythatthesamplecontainsexactlythreestudentswholiveinthedormitories? b.Whatistheprobabilitythatthesamplecontainsnostudentswholivesinthedormitories? c.Whatistheprobabilitythatthesamplecontainsmorethanthreestudentswhodonotliveinthedormitories? d.Whatistheexpectednumberofstudents(inthesample)whodonotliveinthedormitories?   109.Amanufacturingcompanyhas5identicalmachinesthatproducenails.Theprobabilitythatamachinewillbreakdownonanygivendayis.1.DefinearandomvariableXtobethenumberofmachinesthatwillbreakdowninaday.     a.WhatistheappropriateprobabilitydistributionforX?ExplainhowXsatisfiesthepropertiesofthedistribution. b.Computetheprobabilitythat4machineswillbreakdown. c.Computetheprobabilitythatatleast4machineswillbreakdown. d.Whatistheexpectednumberofmachinesthatwillbreakdowninaday? e.Whatisthevarianceofthenumberofmachinesthatwillbreakdowninaday?       .
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    91.RefertoExhibit6-6.WhatistheprobabilitythatarandomlyselectedindividualwithanMBAdegreewillgetastartingsalaryofatleast$30,000? a.0.4772 b.0.9772 c.0.0228 d.0.5000       92.RefertoExhibit6-6.WhatistheprobabilitythatarandomlyselectedindividualwithanMBAdegreewillgetastartingsalaryofatleast$47,500? a.0.4332 b.0.9332 c.0.0668 d.0.5000     93.RefertoExhibit6-6.WhatpercentageofMBA'swillhavestartingsalariesof$34,000to$46,000?a.38.49% b.38.59% c.50% d.76.98%         Exhibit6-7 Theweightofitemsproducedbyamachineisnormallydistributedwithameanof8ouncesandastandarddeviationof2ounces. 94.RefertoExhibit6-7.Whatistheprobabilitythatarandomlyselecteditemwillweighmorethan10ounces?a.0.3413 b.0.8413 c.0.1587 d.0.5000       95.RefertoExhibit6-7.Whatistheprobabilitythatarandomlyselecteditemwillweighbetween11and12ounces?a.0.4772 b.0.4332 c.0.9104 d.0.0440     96.RefertoExhibit6-7.Whatpercentageofitemswillweighatleast11.7ounces?a.46.78% b.96.78% c.3.22% d.53.22%     97.RefertoExhibit6-7.Whatpercentageofitemswillweighbetween6.4and8.9ounces?a.0.1145 b.0.2881 c.0.1736 d.0.4617     98.RefertoExhibit6-7.Whatistheprobabilitythatarandomlyselecteditemweighsexactly8ounces?a.0.5 b.1.0 c.0.3413 d.0.0000         Exhibit6-8 Thelifeexpectancyofaparticularbrandoftireisnormallydistributedwithameanof40,000andastandarddeviationof5,000miles. 99.RefertoExhibit6-8.Whatistheprobabilitythatarandomlyselectedtirewillhavealifeofatleast30,000miles?a.0.4772 b.0.9772 c.0.0228 d.0.5000       100.RefertoExhibit6-8.Whatistheprobabilitythatarandomlyselectedtirewillhavealifeofatleast47,500miles?a.0.4332 b.0.9332 c.0.0668 d.0.4993       .
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  121.Aproductionprocessproduces2%defectiveparts.Asampleof5partsfromtheproductionisselected.Whatistheprobabilitythatthesamplecontainsexactlytwodefectiveparts?Usethebinomialprobabilityfunctionandshowyourcomputationstoanswerthisquestion.   122.AretailerofelectronicequipmentreceivedsixVCRsfromthemanufacturer.ThreeoftheVCRsweredamagedintheshipment.TheretailersoldtwoVCRstotwocustomers.   a.Canabinomialformulabeusedforthesolutionoftheaboveproblem? b.Whatkindofprobabilitydistributiondoestheabovesatisfy,andisthereafunctionforsolvingsuchproblems? c.WhatistheprobabilitythatbothcustomersreceiveddamagedVCRs? d.WhatistheprobabilitythatoneofthetwocustomersreceivedadefectiveVCR?     123.Themanagementofagrocerystorehaskeptarecordofbadchecksreceivedperdayforaperiodof200days.Thedataareshownbelow.         NumberofBadChecks Received   NumberofDays 08 112 220 360 440 530 620 710     a.Developaprobabilitydistributionfortheabovedata. b.IstheprobabilitydistributionthatyoufoundinPart“a”aproperprobabilitydistribution?Explain. c.DeterminethecumulativeprobabilitydistributionF(x). d.Whatistheprobabilitythatinagivendaythestorereceivesfourorlessbadchecks? e.Whatistheprobabilitythatinagivendaythestorereceivesmorethan3badchecks?       124.ThefollowingprobabilitydistributionrepresentsthenumberofgrievancesfiledpermonthwiththeMNM.Corporation.   xf(x) 00.04 10.36 20.50 30.08 40.02   a.Determinetheexpectedvalueofthenumberofgrievancesinamonth. b.Determinethevariance. c.Computethestandarddeviation.       .
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  130.Thelengthoftimepatientsmustwaittoseeadoctorinalocalclinicisuniformlydistributedbetween15minutesand21/2hours.   a.Whatistheprobabilityofapatientwaitingexactly50minutes? b.Whatistheprobabilitythatapatientwouldhavetowaitbetween45minutesand2hours? c.Computetheprobabilitythatapatientwouldhavetowaitover2hours. d.Determinetheexpectedwaitingtimeanditsstandarddeviation.   131.ThemonthlyincomeofresidentsofDaisyCityisnormallydistributedwithameanof$3000andastandarddeviationof$500.     a.ThemayorofDaisyCitymakes$2,250amonth.WhatpercentageofDaisyCity'sresidentshasincomesthataremorethanthemayor's? b.Individualswithincomesoflessthan$1,985permonthareexemptfromcitytaxes.Whatpercentageofresidentsisexemptfromcitytaxes? c.Whataretheminimumandthemaximumincomesofthemiddle95%oftheresidents? d.Twohundredresidentshaveincomesofatleast$4,440permonth.WhatisthepopulationofDaisyCity?   132.Zisastandardnormalrandomvariable.Computethefollowingprobabilities.   a.P(-1.33Z1.67) b.P(1.23Z1.55) c.P(Z2.32) d.P(Z-2.08) e.P(Z-1.08)         133.Thelengthoftimeittakesstudentstocompleteastatisticsexaminationisuniformlydistributedandvariesbetween40and60minutes.   a.Findthemathematicalexpressionfortheprobabilitydensityfunction. b.Computetheprobabilitythatastudentwilltakebetween45and50minutestocompletetheexamination. c.Computetheprobabilitythatastudentwilltakenomorethan40minutestocompletetheexamination. d.Whatistheexpectedamountoftimeittakesastudenttocompletetheexamination? e.Whatisthevariancefortheamountoftimeittakesastudenttocompletetheexamination? 134.Theadvertisedweightonacanofsoupis10ounces.Theactualweightinthecansfollowsauniformdistributionandvariesbetween9.3and10.3ounces.   a.Givethemathematicalexpressionfortheprobabilitydensityfunction. b.Whatistheprobabilitythatacanofsoupwillhavebetween9.4and10.3ounces? c.Whatisthemeanweightofacanofsoup? d.Whatisthestandarddeviationoftheweight?       .
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    71.Theprobabilityassignedtoeachexperimentaloutcomemustbe a.anyvaluelargerthanzero b.smallerthanzero c.atleastone d.betweenzeroandone   72.IfP(A)=0.58,P(B)=0.44,andP(A∩B)=0.25,thenP(A∪B)=a.1.02 b.0.77 c.0.11 d.0.39     73.IfP(A)=0.50,P(B)=0.60,andP(A∩B)=0.30,theneventsAandBare a.mutuallyexclusiveevents b.notindependentevents c.independentevents d.notenoughinformationisgiventoanswerthisquestion       74.IfP(A)=0.62,P(B)=0.47,andP(A∪B)=0.88,thenP(A∩B)=a.0.2914 b.1.9700 c.0.6700 d.0.2100   75.IfP(A)=0.68,P(A∪B)=0.91,andP(A∩B)=0.35,thenP(B)=a.0.22 b.0.09 c.0.65 d.0.58   76.IfAandBareindependenteventswithP(A)=0.4andP(B)=0.25,thenP(A∪B)=a.0.65 b.0.55 c.0.10 d.0.75     77.Ifapennyistossedthreetimesandcomesupheadsallthreetimes,theprobabilityofheadsonthefourthtrialis a.smallerthantheprobabilityoftails b.largerthantheprobabilityoftailsc.1/16 d.1/2       78.IfP(A)=0.50,P(B)=0.40,then,andP(A∪B)=0.88,thenP(B|A)=a.0.02 b.0.03 c.0.04 d.0.05     79.IfAandBareindependenteventswithP(A)=0.38andP(B)=0.55,thenP(A|B)=a.0.209 b.0.000 c.0.550 d.0.38       80.IfXandYaremutuallyexclusiveeventswithP(X)=0.295,P(Y)=0.32,thenP(X|Y)=a.0.0944 b.0.6150 c.1.0000 d.0.0000       .
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    101.RefertoExhibit6-8.Whatpercentageoftireswillhavealifeof34,000to46,000miles?a.38.49% b.76.98% c.50% d.88.49%     102.RefertoExhibit6-8.Whatistheprobabilitythatarandomlyselectedtirewillhavealifeofexactly47,500miles?a.0.0000 b.0.9332 c.0.0668 d.0.4993     Exhibit6-9 TheaveragepriceofpersonalcomputersmanufacturedbyMNMCompanyis$1,200withastandarddeviationof $220.Furthermore,itisknownthatthecomputerpricesmanufacturedbyMNMarenormallydistributed. 103.RefertoExhibit6-9.Whatistheprobabilitythatarandomlyselectedcomputerwillhaveapriceofatleast$1,530?a.0.0668 b.0.5668 c.0.4332 d.1.4332         104.RefertoExhibit6-9.Computerswithpricesofmorethan$1,750receiveadiscount.Whatpercentageofthecomputerswillreceivethediscount? a.62% b.0.62% c.0.062% d.99.38%     105.RefertoExhibit6-9.Whatistheminimumvalueofthemiddle95%ofcomputerprices?a.$1,768.80 b.$1,295.80c.$2,400.00d.$768.80   106.RefertoExhibit6-9.If513oftheMNMcomputerswerepricedatorbelow$647.80,howmanycomputerswereproducedbyMNM? a.185,500 b.85,500 c.513,000 d.notenoughinformationisprovidedtoanswerthisquestion     Exhibit6-10 Aprofessoratalocaluniversitynotedthatthegradesofherstudentswerenormallydistributedwithameanof73andastandarddeviationof11. 107.RefertoExhibit6-10.Theprofessorhasinformedusthat7.93percentofherstudentsreceivedgradesofA.WhatistheminimumscoreneededtoreceiveagradeofA? a.90.51 b.93.2 c.88.51 d.100.00       108.RefertoExhibit6-10.Studentswhomade57.93orlowerontheexamfailedthecourse.Whatpercentofstudentsfailedthecourse? a.8.53% b.18.53% c.91.47% d.0.853%       109.RefertoExhibit6-10.If69.5percentofthestudentsreceivedgradesofCorbetter,whatistheminimumscoreofthosewhoreceivedC's? a.70.39 b.67.39 c.50.39 d.65.39         .
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  95.Aproductionprocessproduces90%non-defectiveparts.Asampleof10partsfromtheproductionprocessisselected.   a.Whatistheprobabilitythatthesamplewillcontain7non-defectiveparts? b.Whatistheprobabilitythatthesamplewillcontainatleast4defectiveparts? c.Whatistheprobabilitythatthesamplewillcontainlessthan5non-defectiveparts? d.Whatistheprobabilitythatthesamplewillcontainnodefectiveparts?       96.Fifty-fivepercentoftheapplicationsreceivedforaparticularcreditcardareaccepted.Amongthenexttwelveapplications,   a.whatistheprobabilitythatallwillberejected? b.whatistheprobabilitythatallwillbeaccepted? c.whatistheprobabilitythatexactly4willbeaccepted? d.whatistheprobabilitythatfewerthan3willbeaccepted? e.Determinetheexpectednumberandthevarianceoftheacceptedapplications.   97.Theprobabilitydistributionofthedailydemandforaproductisshownbelow.     DemandProbability 00.05 10.10 20.15 30.35 40.20 50.10 60.05     a.Whatistheexpectednumberofunitsdemandedperday? b.Determinethevarianceandthestandarddeviation. 98.Inalargecorporation,65%oftheemployeesaremale.Arandomsampleoffiveemployeesisselected.UsetheBinomialprobabilitytablestoanswerthefollowingquestions.   a.Whatistheprobabilitythatthesamplecontainsexactlythreemaleemployees? b.Whatistheprobabilitythatthesamplecontainsnomaleemployees? c.Whatistheprobabilitythatthesamplecontainsmorethanthreefemaleemployees? d.Whatistheexpectednumberoffemaleemployeesinthesample?       99.Forthefollowingprobabilitydistribution:     xf(x) 00.01 10.02 20.10 30.35 40.20 50.11 60.08 70.05 80.04 90.03 100.01     a.DetermineE(x). b.Determinethevarianceandthestandarddeviation.       .
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    31.IfAandBareindependenteventswithP(A)=0.65andP(A∩B)=0.26,then,P(B)=a.0.400 b.0.169 c.0.390 d.0.650       32.IfP(A)=0.4,P(B|A)=0.35,P(A∪B)=0.69,thenP(B)=a.0.14 b.0.43 c.0.75 d.0.59       33.Offiveletters(A,B,C,D,andE),twolettersaretobeselectedatrandom.Howmanypossibleselectionsarethere? a.20 b.7 c.5! d.10     34.GiventhateventEhasaprobabilityof0.31,theprobabilityofthecomplementofeventE a.cannotbedeterminedwiththeaboveinformation b.canhaveanyvaluebetweenzeroandonec.0.69 d.is 0.31     35.Threeapplicationsforadmissiontoalocaluniversityarechecked,anditisdeterminedwhethereachapplicantismaleorfemale.Thenumberofsamplepointsinthisexperimentis a.2 b.4 c.6 d.8     36.Assumeyourfavoritefootballteamhas2gameslefttofinishtheseason.Theoutcomeofeachgamecanbewin,loseortie.Thenumberofpossibleoutcomesis a.2 b.4 c.6 d.9       37.Eachcustomerenteringadepartmentstorewilleitherbuyornotbuysomemerchandise.Anexperimentconsistsoffollowing3customersanddeterminingwhetherornottheypurchaseanymerchandise.Thenumberofsamplepointsinthisexperimentis a.2 b.4 c.6 d.8       38.Anexperimentconsistsoftossing4coinssuccessively.Thenumberofsamplepointsinthisexperimentis a.16 b.8 c.4 d.2     39.Anexperimentconsistsofthreesteps.Therearefourpossibleresultsonthefirststep,threepossibleresultsonthesecondstep,andtwopossibleresultsonthethirdstep.Thetotalnumberofexperimentaloutcomesis a.9 b.14 c.24 d.36     40.Sincethesunmustrisetomorrow,thentheprobabilityofthesunrisingtomorrowis a.muchlargerthanone b.zero c.infinity d.Noneofthesealternativesiscorrect.       .
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    31.Inabinomialexperiment a.theprobabilitydoesnotchangefromtrialtotrial b.theprobabilitydoeschangefromtrialtotrial c.theprobabilitycouldchangefromtrialtotrial,dependingonthesituationunderconsideration d.Noneofthesealternativesiscorrect.     32.Assumethatyouhaveabinomialexperimentwithp=0.5andasamplesizeof100.Theexpectedvalueofthisdistributionis a.0.50 b.0.30 c.100 d.50     33.Whichofthefollowingisnotapropertyofabinomialexperiment? a.theexperimentconsistsofasequenceofnidenticaltrials b.eachoutcomecanbereferredtoasasuccessorafailure c.theprobabilitiesofthetwooutcomescanchangefromonetrialtothenext d.thetrialsareindependent     34.ThePoissonprobabilitydistributionisusedwith a.acontinuousrandomvariable b.adiscreterandomvariable c.eitheracontinuousordiscreterandomvariable d.anyrandomvariable     35.Thestandarddeviationofabinomialdistributionisa.σ(x)=P(1-P) b.σ(x)=nP c.σ(x)=nP(1-P) d.Noneofthesealternativesiscorrect.       36.Theexpectedvalueforabinomialprobabilitydistributionis a.E(x)=Pn(1-n)b.E(x)=P(1-P) c.E(x)=nP d.E(x)=nP(1-P)     37.Thevarianceforthebinomialprobabilitydistributionis a.var(x)=P(1-P) b.var(x)=nP c.var(x)=n(1-P) d.var(x)=nP(1-P)     38.Aproductionprocessproduces2%defectiveparts.Asampleoffivepartsfromtheproductionprocessisselected.Whatistheprobabilitythatthesamplecontainsexactlytwodefectiveparts? a.0.0004 b.0.0038 c.0.10 d.0.02     39.Whendealingwiththenumberofoccurrencesofaneventoveraspecifiedintervaloftimeorspace,theappropriateprobabilitydistributionisa a.binomialdistribution b.Poissondistribution c.normaldistribution d.hypergeometricprobabilitydistribution     40.Thehypergeometricprobabilitydistributionisidenticalto a.thePoissonprobabilitydistribution b.thebinomialprobabilitydistribution c.thenormaldistribution d.Noneofthesealternativesiscorrect.         .
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    81.RefertoExhibit6-3.TheprobabilitythatXwilltakeonavaluebetween21and25isa.0.125 b.0.250 c.0.500 d.1.000     82.RefertoExhibit6-3.TheprobabilitythatXwilltakeonavalueofatleast26isa.0.000 b.0.125 c.0.250 d.1.000     83.RefertoExhibit6-3.ThemeanofXisa.0.000 b.0.125 c.23 d.24         84.RefertoExhibit6-3.ThevarianceofXisapproximatelya.2.309 b.5.333 c.32 d.0.667       Exhibit6-4 f(x)=(1/10)e-x/10x≥0 85.RefertoExhibit6-4.Themeanofxisa.0.10 b.10c.100 d.1,000       86.RefertoExhibit6-4.Theprobabilitythatxisbetween3and6isa.0.4512 b.0.1920 c.0.2592 d.0.6065     87.RefertoExhibit6-4.Theprobabilitythatxislessthan5isa.0.6065 b.0.0606 c.0.3935 d.0.9393     Exhibit6-5 Thetraveltimeforacollegestudenttravelingbetweenherhomeandhercollegeisuniformlydistributedbetween40and90minutes. 88.RefertoExhibit6-5.Theprobabilitythatshewillfinishhertripin80minutesorlessisa.0.02 b.0.8 c.0.2 d.1.00         89.RefertoExhibit6-5.Theprobabilitythathertripwilltakelongerthan60minutesisa.1.00 b.0.40 c.0.02 d.0.600     90.RefertoExhibit6-5.Theprobabilitythathertripwilltakeexactly50minutesis a.zerob.0.02c.0.06d.0.20   Exhibit6-6 ThestartingsalariesofindividualswithanMBAdegreearenormallydistributedwithameanof$40,000andastandarddeviationof$5,000.   .
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  135.Zisastandardnormalrandomvariable.Computethefollowingprobabilities.   a.P(-1.23Z2.58) b.P(1.83Z1.96)           g.P(-2.37 Z-1.54)h.P(Z=2.56)   136.Themiles-per-gallonobtainedbythe1995modelZcarsisnormallydistributedwithameanof22miles-per-gallonandastandarddeviationof5miles-per-gallon.   a.Whatistheprobabilitythatacarwillgetbetween13.35and35.1miles-per-gallon? b.Whatistheprobabilitythatacarwillgetmorethan29.6miles-per-gallon? c.Whatistheprobabilitythatacarwillgetlessthan21miles-per-gallon? d.Whatistheprobabilitythatacarwillgetexactly22miles-per-gallon?   137.Thesalariesatacorporationarenormallydistributedwithanaveragesalaryof$19,000andastandarddeviationof $4,000.   a.Whatistheprobabilitythatanemployeewillhaveasalarybetween$12,520and$13,480? b.Whatistheprobabilitythatanemployeewillhaveasalarymorethan$11,880? c.Whatistheprobabilitythatanemployeewillhaveasalarylessthan$28,440?     138.Zisastandardnormalvariable.FindthevalueofZinthefollowing.   a.Theareabetween0andZis0.4678. b.TheareatotherightofZis0.1112. c.TheareatotheleftofZis0.8554 d.Theareabetween-ZandZis0.754. e.Theareatotheleftof-Zis0.0681. f.Theareatotherightof-Zis0.9803.       .
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  SubjectiveShortAnswer 110.TheaveragepriceofcellphonesmanufacturedbyAhmadi,Inc.is$98withastandarddeviationof$12.Furthermore,itisknownthatthepricesofthecellphonesmanufacturedbyAhmadiarenormallydistributed. a.WhatpercentageofcellphonesproducedbyAhmadi,Inc.willhavepricesofatleast$120.20? b.Cellphoneswithpricesofatleast81.80willgetafreegift.Whatpercentageofthecellphoneswillbeeligibleforthefreegift? c.Whataretheminimumandthemaximumvaluesofthemiddle95%ofcellphoneprices? d.If7,218oftheAhmadicellphoneswerepricedatleast$119.00,howmanycellphoneswereproducedbyAhmadi,Inc.?       111.Thedrivingtimeforanindividualfromhishometohisworkisuniformlydistributedbetween300to480seconds.   a.Determinetheprobabilitydensityfunction. b.Computetheprobabilitythatthedrivingtimewillbelessthanorequalto435seconds. c.Determinetheexpecteddrivingtime. d.Computethevariance. e.Computethestandarddeviation.       112.TheBodyPaint,anautomobilebodypaintshop,hasdeterminedthatthepaintingtimeofautomobilesisuniformlydistributedandthattherequiredtimerangesbetween45minutesto1hours. a.Giveamathematicalexpressionfortheprobabilitydensityfunction. b.Whatistheprobabilitythatthepaintingtimewillbelessthanorequaltoonehour? c.Whatistheprobabilitythatthepaintingtimewillbemorethan50minutes? d.Determinetheexpectedpaintingtimeanditsstandarddeviation. 113.Forastandardnormaldistribution,determinetheprobabilitiesofobtainingthefollowingzvalues.Itishelpfultodrawanormaldistributionforeachcaseandshowthecorrespondingarea.   a.Greaterthanzero b.Between-2.4and-2.0 c.Lessthan1.6 d.Between-1.9to1.7 e.Between1.5and1.75   114.Aprofessoratalocalcommunitycollegenotedthatthegradesofhisstudentswerenormallydistributedwithameanof74andastandarddeviationof10.Theprofessorhasinformedusthat6.3percentofhisstudentsreceivedA'swhileonly2.5percentofhisstudentsfailedthecourseandreceivedF's.   a.WhatistheminimumscoreneededtomakeanA? b.WhatisthemaximumscoreamongthosewhoreceivedanF? c.Iftherewere5studentswhodidnotpassthecourse,howmanystudentstookthecourse?           .
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    51.RefertoExhibit5-2.Whatistheprobabilitythatamongthestudentsinthesampleatleast6aremale?a.0.0413 b.0.0079 c.0.0007 d.0.0499     Exhibit5-3 Rothisacomputer-consultingfirm.Thenumberofnewclientsthattheyhaveobtainedeachmonthhasrangedfrom0to6.Thenumberofnewclientshastheprobabilitydistributionthatisshownbelow.     NumberofNewClients   Probability 00.05 10.10 20.15 30.35 40.20 50.10 60.05 52.RefertoExhibit5-3.Theexpectednumberofnewclientspermonthis a.6 b.0 c.3.05 d.21       53.RefertoExhibit5-3.Thevarianceisa.1.431 b.2.047 c.3.05 d.21       54.RefertoExhibit5-3.Thestandarddeviationisa.1.431 b.2.047 c.3.05 d.21       Exhibit5-4 Fortypercentofallregisteredvotersinanationalelectionarefemale.Arandomsampleof5votersisselected. 55.RefertoExhibit5-4.Theprobabilitythatthesamplecontains2femalevotersisa.0.0778 b.0.7780 c.0.5000 d.0.3456       56.RefertoExhibit5-4.Theprobabilitythattherearenofemalesinthesampleisa.0.0778 b.0.7780 c.0.5000 d.0.3456     Exhibit5-5 ProbabilityDistribution     xf(x) 10.2 20.3 30.4 40.1 57.RefertoExhibit5-5.Theexpectedvalueofxequals a.24 b.25 c.30d.100     58.RefertoExhibit5-5.Thevarianceofxequalsa.9.165 b.84 c.85 d.93.33       Exhibit5-6 Asampleof2,500peoplewasaskedhowmanycupsofcoffeetheydrinkinthemorning.Youaregiventhefollowingsampleinformation.     CupsofCoffeeFrequency 0700 1900 2600 3300 2,500 59.RefertoExhibit5-6.Theexpectednumberofcupsofcoffeeis a.1b.1.2c.1.5d.1.7     60.RefertoExhibit5-6.Thevarianceofthenumberofcupsofcoffeeisa..96 b..9798 c.1d.2.4   Exhibit5-7 TheprobabilitythatPetewillcatchfishwhenhegoesfishingis.8.Peteisgoingtofish3daysnextweek.DefinetherandomvariableXtobethenumberofdaysPetecatchesfish.   .
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  105.Startingsalariesofasampleoffivemanagementmajorsalongwiththeirgendersareshownbelow.   Salary Employee(in$1,000s)Gender 130F 228M 322F 426F 519M       a.Whatisthepointestimateforthestartingsalariesofallmanagementmajors? b.Determinethepointestimateforthevarianceofthepopulation. c.Determinethepointestimatefortheproportionofmaleemployees.   106.Anexperimentaldiettoinduceweightlosswasfollowedforoneweekbyarandomlyselectedgroupof12studentswiththefollowingresults.     StudentLossinPounds 12.2 22.6 30.4 42.0 50.0 61.8 75.2 83.8 94.2 103.8 111.4 122.6     a.Findapointestimatefortheaverageamountlostafteroneweekonthisdiet.Isthisanunbiasedestimateofthepopulationmean?Explain. b.Findapointestimateforthevarianceoftheamountlostonthisdiet.Isthisanunbiasedestimateofthepopulationvariance?Explain. c.Findapointestimateforthestandarddeviationoftheamountlostonthisdiet. 107.Belowyouaregiventhevaluesobtainedfromarandomsampleof4observationstakenfromaninfinitepopulation.32343539 a.Findapointestimateforμ.Isthisanunbiasedestimateofμ? Explain. b.Findapointestimateforσ2.Isthisanunbiasedestimateofσ2? Explain. c.Findapointestimateforσ. d.Whatcanbesaidaboutthesamplingdistributionof?Besuretodiscusstheexpectedvalue,thestandarddeviation,andtheshapeofthesamplingdistributionof. d.E()=μ,thestandarddeviation=σ2/n, andthesamplingdistribution ofisnormallydistributedifthepopulationisnormallydistributed.     108.Thefollowinginformationgivesthenumberofdaysabsentfromworkforapopulationof5workersatasmallfactory.     WorkerNumberofDaysAbsent A5 B7 C1 D4 E8     a.Findthemeanandthestandarddeviationforthepopulation. b.Samplesofsize2willbedrawnfromthepopulation.Usetheanswersinpartatocalculatetheexpectedvalueandthestandarddeviationofthesamplingdistributionofthesamplemean. c.Findallthesamplesof2workersthatcanbeextractedfromthispopulation.Choosethesampleswithoutreplacement. d.Computethesamplemean foreachofthesamplesinPartc. 109.MNMCorporationgiveseachofitsemployeesanaptitudetest.Thescoresonthetestarenormallydistributedwithameanof75andastandarddeviationof15.Asimplerandomsampleof25istakenfromapopulationof500.     a.Whataretheexpectedvalue,thestandarddeviation,andtheshapeofthesamplingdistributionof? b.Whatistheprobabilitythattheaverageaptitudetestinthesamplewillbebetween70.14and82.14? c.Whatistheprobabilitythattheaverageaptitudetestinthesamplewillbegreaterthan82.68? d.Whatistheprobabilitythattheaverageaptitudetestinthesamplewillbelessthan78.69? e.Findavalue,C,suchthatP( ≥ C)=.015.             .
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    41.Assumethatyouhaveabinomialexperimentwithp=0.5andasamplesizeof100.Thevalueofthestandarddeviationis a.50 b.2 c.25 d.5       42.Thekeydifferencebetweenthebinomialandhypergeometricdistributionisthatwiththehypergeometricdistribution a.theprobabilityofsuccessmustbelessthan0.5 b.theprobabilityofsuccesschangesfromtrialtotrial c.thetrialsareindependentofeachother d.therandomvariableiscontinuous     43.Assumethatyouhaveabinomialexperimentwithp=0.4andasamplesizeof50.Thevarianceofthisdistributionis a.20 b.12c.3.46d.144   44.Inabinomialexperimenttheprobabilityofsuccessis0.06.Whatistheprobabilityoftwosuccessesinseventrials?a.0.0036 b.0.0600 c.0.0555 d.0.2800     45.Xisarandomvariablewiththeprobabilityfunction:f(X)=X/6forX =1,2or 3 TheexpectedvalueofXisa.0.333 b.0.500 c.2.000 d.2.333       46.Arandomvariablethatmaytakeonanyvalueinanintervalorcollectionofintervalsisknownasa a.continuousrandomvariable b.discreterandomvariable c.continuousprobabilityfunction d.finiteprobabilityfunction       Exhibit5-1 Thefollowingrepresentstheprobabilitydistributionforthedailydemandofcomputersatalocalstore.     DemandProbability 00.1 10.2 20.3 30.2 40.2 47.RefertoExhibit5-1.Theexpecteddailydemandis a.1.0 b.2.2 c.2,sinceithasthehighestprobability d.ofcourse4,sinceitisthelargestdemandlevel       48.RefertoExhibit5-1.Theprobabilityofhavingademandforatleasttwocomputersisa.0.7 b.0.3 c.0.4 d.1.0     Exhibit5-2 Thestudentbodyofalargeuniversityconsistsof60%femalestudents.Arandomsampleof8studentsisselected. 49.RefertoExhibit5-2.Whatistheprobabilitythatamongthestudentsinthesampleexactlytwoarefemale?a.0.0896 b.0.2936 c.0.0413 d.0.0007       50.RefertoExhibit5-2.Whatistheprobabilitythatamongthestudentsinthesampleatleast7arefemale?a.0.1064 b.0.0896 c.0.0168 d.0.8936         .
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  120.TheGlobeFisherypacksshrimpthatweighmorethan1.91ounceseachinpackagesmarked"large"andshrimpthatweighlessthan0.47ounceseachintopackagesmarked"small";theremainderarepackedin"medium"sizepackages.Ifaday'scatchshowedthat19.77percentoftheshrimpwerelargeand6.06percentweresmall,determinethemeanandthestandarddeviationfortheshrimpweights.Assumethattheshrimps'weightsarenormallydistributed.   121.Themonthlyearningsofcomputerprogrammersarenormallydistributedwithameanof$4,000.Ifonly1.7percentofprogrammershavemonthlyincomesoflessthan$2,834,whatisthevalueofthestandarddeviationofthemonthlyearningsofthecomputerprogrammers?   122.Amajordepartmentstorehasdeterminedthatitscustomerschargeanaverageof$500permonth,withastandarddeviationof$80.Assumetheamountsofchargesarenormallydistributed.   a.Whatpercentageofcustomerschargesmorethan$380permonth? b.Whatpercentageofcustomerschargeslessthan$340permonth? c.Whatpercentageofcustomerschargesbetween$644and$700permonth?       123.TheFirstNationalMortgageCompanyhasnotedthat6%ofitscustomerspaytheirmortgagepaymentsaftertheduedate.     a.Whatistheprobabilitythatinarandomsampleof150customers7willbelateontheirpayments? b.Whatistheprobabilitythatinarandomsampleof150customersatleast10willbelateontheirpayments?     124.Thesalariesoftheemployeesofacorporationarenormallydistributedwithameanof$25,000andastandarddeviationof$5,000.   a.Whatistheprobabilitythatarandomlyselectedemployeewillhaveastartingsalaryofatleast $31,000? b.Whatpercentageofemployeeshassalariesoflessthan$12,200? c.Whataretheminimumandthemaximumsalariesofthemiddle95%oftheemployees? d.Ifsixty-eightoftheemployeeshaveincomesofatleast$35,600,howmanyindividualsareemployedinthecorporation?       .
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    51.Anexponentialprobabilitydistribution a.isacontinuousdistribution b.isadiscretedistribution c.canbeeithercontinuousordiscrete d.mustbenormallydistributed     52.Zisastandardnormalrandomvariable.WhatisthevalueofZiftheareatotherightofZis0.1112?a.0.3888 b.1.22 c.2.22 d.3.22         53.Zisastandardnormalrandomvariable.WhatisthevalueofZiftheareabetween-ZandZis0.754?a.0.377 b.0.123 c.2.16 d.1.16     54.Zisastandardnormalrandomvariable.WhatisthevalueofZiftheareatotherightofZis0.9803?a.-2.06 b.0.4803 c.0.0997 d.3.06     55.Forastandardnormaldistribution,theprobabilityofobtainingazvaluebetween-2.4to-2.0isa.0.4000 b.0.0146 c.0.0400 d.0.5000     56.Forastandardnormaldistribution,theprobabilityofobtainingazvalueoflessthan1.6isa.0.1600 b.0.0160 c.0.0016 d.0.9452     57.Forastandardnormaldistribution,theprobabilityofobtainingazvaluebetween-1.9to1.7isa.0.9267 b.0.4267 c.1.4267 d.0.5000         58.Theagesofstudentsatauniversityarenormallydistributedwithameanof21.Whatpercentageofthestudentbodyisatleast21yearsold? a.Itcouldbeanyvalue,dependingonthemagnitudeofthestandarddeviationb.50% c.21% d.1.96%     59.Zisastandardnormalrandomvariable.TheP(1.05≤ Z≤ 2.13)equalsa.0.8365 b.0.1303 c.0.4834 d.0.3531     60.Zisastandardnormalrandomvariable.TheP(Z≥ 2.11)equalsa.0.4821 b.0.9821 c.0.5 d.0.0174       .
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  130.Onarecentholidayevening,asampleof500driverswasstoppedbythepolice.Threehundredwereunder30yearsofage.Atotalof250wereundertheinfluenceofalcohol.Ofthedriversunder30yearsofage,200wereundertheinfluenceofalcohol.   LetAbetheeventthatadriverisundertheinfluenceofalcohol.LetYbetheeventthatadriverislessthan30yearsold.   a.DetermineP(A)andP(Y). b.Whatistheprobabilitythatadriverisunder30andnotundertheinfluenceofalcohol? c.Giventhatadriverisnotunder30,whatistheprobabilitythathe/sheisundertheinfluenceofalcohol? d.Whatistheprobabilitythatadriverisundertheinfluenceofalcohol,whenweknowthedriverisunder30? e.Showthejointprobabilitytable. f.AreAandYmutuallyexclusiveevents?Explain. g.AreAandYindependentevents?Explain.       131.YouaregiventhefollowinginformationonEventsA,B,C,andD.     P(A)=.4P(A?D)=.6 P(B)=.2P(A|B)=.3 P(C)=.1P(A∩C)=.04P(A∩D)=.03     a.ComputeP(D). b.ComputeP(A∩B). c.ComputeP(A|C). d.ComputetheprobabilityofthecomplementofC. e.AreAandBmutuallyexclusive?Explainyouranswer. f.AreAandBindependent?Explainyouranswer. g.AreAandCmutuallyexclusive?Explainyouranswer. h.AreAandCindependent?Explainyouranswer. 132.Inacity,60%oftheresidentsliveinhousesand40%oftheresidentsliveinapartments.Ofthepeoplewholiveinhouses,20%owntheirownbusiness.Ofthepeoplewholiveinapartments,10%owntheirownbusiness.Ifapersonownshisorherownbusiness,findtheprobabilitythatheorshelivesinahouse.   133.Fourworkersatafastfoodrestaurantpackthetake-outchickendinners.Johnpacks45%ofthedinnersbutfailstoincludeasaltpacket4%ofthetime.Marypacks25%ofthedinnersbutomitsthesalt2%ofthetime.Suepacks30%ofthedinnersbutfailstoincludethesalt3%ofthetime.Youhavepurchasedadinnerandthereisnosalt.   a.FindtheprobabilitythatJohnpackedyourdinner. b.FindtheprobabilitythatMarypackedyourdinner.   134.Astatisticsprofessorhasnotedfrompastexperiencethatastudentwhofollowsaprogramofstudyingtwohoursforeachhourinclasshasaprobabilityof0.9ofgettingagradeofCorbetter,whileastudentwhodoesnotfollowaregularstudyprogramhasaprobabilityof0.2ofgettingaCorbetter.Itisknownthat70%ofthestudentsfollowthestudyprogram.FindtheprobabilitythatastudentwhohasearnedaCorbettergrade,followedtheprogram.   135.AlltheemployeesofABCCompanyareassignedIDnumbers.TheIDnumberconsistsofthefirstletterofanemployee'slastname,followedbyfournumbers.   a.HowmanypossibledifferentIDnumbersarethere? b.HowmanypossibledifferentIDnumbersarethereforemployeeswhoselastnamestartswithanA?     136.Assumeyouhaveappliedtotwodifferentuniversities(let'srefertothemasUniversitiesAandB)foryourgraduatework.Inthepast,25%ofstudents(withsimilarcredentialsasyours)whoappliedtoUniversityAwereaccepted,whileUniversityBaccepted35%oftheapplicants.Assumeeventsareindependentofeachother.   a.Whatistheprobabilitythatyouwillbeacceptedinbothuniversities? b.Whatistheprobabilitythatyouwillbeacceptedtoatleastonegraduateprogram? c.Whatistheprobabilitythatoneandonlyoneoftheuniversitieswillacceptyou? d.Whatistheprobabilitythatneitheruniversitywillacceptyou?     .
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    21.Ifyouareconductinganexperimentwheretheprobabilityofasuccessis0.2perdayandyouareinterestedinfindingtheprobabilityof4successesininthreedays,thecorrectprobabilityfunctiontouseis a.thestandardnormalprobabilitydensityfunction b.thenormalprobabilitydensityfunction c.thePoissonprobabilityfunction d.anyprobabilityaslongasthetablesareavailable     22.Whichofthefollowingstatementsaboutadiscreterandomvariableanditsprobabilitydistributionaretrue? a.Valuesoftherandomvariablecanneverbenegative. b.Somenegativevaluesoff(x)areallowedaslongas∑f(x)=1. c.Valuesoff(x)mustbegreaterthanorequaltozero. d.Thevaluesoff(x)increasetoamaximumpointandthendecrease.     23.Inthetextileindustry,amanufacturerisinterestedinthenumberofblemishesorflawsoccurringineach100feetofmaterial.Theprobabilitydistributionthathasthegreatestchanceofapplyingtothissituationisthe a.normaldistribution b.binomialdistribution c.Poissondistribution d.uniformdistribution     24.ThePoissonprobabilitydistributionisa a.continuousprobabilitydistribution b.discreteprobabilitydistribution c.uniformprobabilitydistribution d.normalprobabilitydistribution     25.Thebinomialprobabilitydistributionisusedwith a.acontinuousrandomvariable b.adiscreterandomvariable c.anydistribution,aslongasitisnotnormal d.Noneofthesealternativesiscorrect.         26.Theexpectedvalueofadiscreterandomvariable a.isthemostlikelyorhighestprobabilityvaluefortherandomvariable b.willalwaysbeoneofthevaluesxcantakeon,althoughitmaynotbethehighestprobabilityvaluefortherandomvariable c.istheaveragevaluefortherandomvariableovermanyrepeatsoftheexperiment d.Noneofthesealternativesiscorrect.     27.Whichofthefollowingisnotacharacteristicofanexperimentwherethebinomialprobabilitydistributionisapplicable? a.theexperimenthasasequenceofnidenticaltrials b.exactlytwooutcomesarepossibleoneachtrial c.thetrialsaredependent d.theprobabilitiesoftheoutcomesdonotchangefromonetrialtoanother     28.Whichofthefollowingisacharacteristicofabinomialexperiment? a.atleast2outcomesarepossible b.theprobabilitychangesfromtrialtotrial c.thetrialsareindependent d.Noneofthesealternativesiscorrect.     29.Assumethatyouhaveabinomialexperimentwithp=0.3andasamplesizeof100.Thevalueofthevarianceis a.30 b.33.33 c.100 d.210     30.Theexpectedvalueofarandomvariableis a.thevalueoftherandomvariablethatshouldbeobservedonthenextrepeatoftheexperiment b.thevalueoftherandomvariablethatoccursmostfrequently c.thesquarerootofthevariance d.Noneofthesealternativesiscorrect.           .
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  125.Amanufacturingprocessproducesitemswhoseweightsarenormallydistributed.Itisknownthat22.57%ofalltheitemsproducedweighbetween100gramsuptothemeanand49.18%weighfromthemeanupto190grams.Determinethemeanandthestandarddeviation.   126.Thedailydinnerbillsinalocalrestaurantarenormallydistributedwithameanof$28andastandarddeviationof $6.   a.Whatistheprobabilitythatarandomlyselectedbillwillbeatleast$39.10? b.Whatpercentageofthebillswillbelessthan$16.90? c.Whataretheminimumandmaximumofthemiddle95%ofthebills? d.Iftwelveofoneday'sbillshadavalueofatleast$43.06,howmanybillsdidtherestaurantcollectonthatday?         127.Thepriceofabondisuniformlydistributedbetween$80and$85.   a.Whatistheprobabilitythatthebondpricewillbeatleast$83? b.Whatistheprobabilitythatthebondpricewillbebetween$81to$90? c.Determinetheexpectedpriceofthebond. d.Computethestandarddeviationforthebondprice.   128.Thepriceofastockisuniformlydistributedbetween$30and$40.   a.Whatistheprobabilitythatthestockpricewillbemorethan$37? b.Whatistheprobabilitythatthestockpricewillbelessthanorequalto$32? c.Whatistheprobabilitythatthestockpricewillbebetween$34and$38? d.Determinetheexpectedpriceofthestock. e.Determinethestandarddeviationforthestockprice.   129.ArandomvariableXisuniformlydistributedbetween45and150.   a.DeterminetheprobabilityofX=48. b.What is the probability of X ≤ 60? c.What is the probability of X ≥ 50? d.DeterminetheexpectedvaleofXanditsstandarddeviation.             .
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  115.Sevenstudentshaveappliedformeritscholarships.Thisyear3meritscholarshipswereawarded.Ifarandomsampleof3applications(fromthepopulationof7)isselected,   a.whatistheprobabilitythat2studentswererecipientsofscholarships? b.whatistheprobabilitythatnostudentsweretherecipientsofscholarship?   116.Determinetheprobabilityofbeingdealt4kingsina5-cardpokerhand.   117.Twentypercentoftheapplicationsreceivedforaparticularpositionarerejected.Whatistheprobabilitythatamongthenextfourteenapplications,   a.nonewillberejected? b.allwillberejected? c.lessthan2willberejected? d.morethanfourwillberejected? e.Determinetheexpectednumberofrejectedapplicationsanditsvariance.     118.AninsurancecompanyhasdeterminedthateachweekanaverageofnineclaimsarefiledintheirAtlantabranch. Whatistheprobabilitythatduringthenextweek   a.exactlysevenclaimswillbefiled? b.noclaimswillbefiled? c.lessthanfourclaimswillbefiled? d.atleasteighteenclaimswillbefiled? 119.Alocaluniversityreportsthat10%oftheirstudentstaketheirgeneraleducationcoursesonapass/failbasis.Assumethatfifteenstudentsareregisteredforageneraleducationcourse.   a.Whatistheexpectednumberofstudentswhohaveregisteredonapass/failbasis? b.Whatistheprobabilitythatexactlyfiveareregisteredonapass/failbasis? c.Whatistheprobabilitythatmorethanfourareregisteredonapass/failbasis? d.Whatistheprobabilitythatlessthantwoareregisteredonapass/failbasis?   120.Only0.02%ofcreditcardholdersofacompanyreportthelossortheftoftheircreditcardseachmonth.Thecompanyhas15,000creditcardsinthecityofMemphis.UsethePoissonprobabilitytablestoanswerthefollowingquestions.WhatistheprobabilitythatduringthenextmonthinthecityofMemphis   a.noonereportsthelossortheftofhisorhercreditcards? b.everycreditcardislostorstolen? c.sixpeoplereportthelossortheftoftheircards? d.atleastninepeoplereportthelossortheftoftheircards? e.Determinetheexpectednumberofreportedlostorstolencreditcards. f.Determinethestandarddeviationforthenumberofreportedlostorstolencards.         .
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    71.RefertoExhibit6-1.Theprobabilityofassemblingtheproductbetween7to9minutesis a.zerob.0.50c.0.20 d.1     72.RefertoExhibit6-1.Theprobabilityofassemblingtheproductinlessthan6minutesis a.zerob.0.50c.0.15 d.1     73.RefertoExhibit6-1.Theprobabilityofassemblingtheproductin7minutesormoreisa.0.25 b.0.75 c.zero d.1         74.RefertoExhibit6-1.Theexpectedassemblytime(inminutes)is a.16 b.2 c.8 d.4     75.RefertoExhibit6-1.Thestandarddeviationofassemblytime(inminutes)isapproximatelya.1.3333 b.1.1547 c.0.1111 d.0.5773     Exhibit6-2 Theweightoffootballplayersisnormallydistributedwithameanof200poundsandastandarddeviationof25pounds. 76.RefertoExhibit6-2.Theprobabilityofaplayerweighingmorethan241.25poundsisa.0.4505 b.0.0495 c.0.9505 d.0.9010       77.RefertoExhibit6-2.Theprobabilityofaplayerweighinglessthan250poundsisa.0.4772 b.0.9772 c.0.0528 d.0.5000     78.RefertoExhibit6-2.Whatpercentofplayersweighbetween180and220pounds?a.28.81% b.0.5762% c.0.281% d.57.62%         79.RefertoExhibit6-2.Whatistheminimumweightofthemiddle95%oftheplayers?a.196 b.151 c.249 d.190     Exhibit6-3 ConsiderthecontinuousrandomvariableX,whichhasauniformdistributionovertheintervalfrom20to28. 80.RefertoExhibit6-3.Theprobabilitydensityfunctionhaswhatvalueintheintervalbetween20and28? a.0 b.0.050 c.0.125 d.1.000         .
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    61.RefertoExhibit5-7.TheprobabilitythatPetewillcatchfishonexactlyonedayisa..008 b..096 c..104 d..8       62.RefertoExhibit5-7.TheprobabilitythatPetewillcatchfishononedayorlessisa..008 b..096 c..104 d..8       63.RefertoExhibit5-7.TheexpectednumberofdaysPetewillcatchfishis a..6 b..8c.2.4 d.3     64.RefertoExhibit5-7.ThevarianceofthenumberofdaysPetewillcatchfishisa..16 b..48 c..8d.2.4   Exhibit5-8 Therandomvariablexisthenumberofoccurrencesofaneventoveranintervaloftenminutes.Itcanbeassumedthattheprobabilityofanoccurrenceisthesameinanytwo-timeperiodsofanequallength.Itisknownthatthemeannumberofoccurrencesintenminutesis5.3. 65.RefertoExhibit5-8.TherandomvariablexsatisfieswhichofthefollowingDiscreteProbabilityDistributions? a.normal b.Poisson c.binomial d.Notenoughinformationisgiventoanswerthisquestion.       66.RefertoExhibit5-8.Theappropriateprobabilitydistributionfortherandomvariableis a.discrete b.continuous c.eitherdiscreteorcontinuousdependingonhowtheintervalisdefined d.Noneofthesealternativesiscorrect.       67.RefertoExhibit5-8.Theexpectedvalueoftherandomvariablexis a.2b.5.3 c.10d.2.30     68.RefertoExhibit5-8.Theprobabilitythatthereare8occurrencesintenminutesisa..0241 b..0771 c..1126 d..9107     69.RefertoExhibit5-8.Theprobabilitythattherearelessthan3occurrencesisa..0659 b..0948 c..1016 d..1239     Exhibit5-9 TheprobabilitydistributionforthedailysalesatMichael'sCo.isgivenbelow.     DailySales(In$1,000s)   Probability 400.1 500.4 600.3 700.2 70.RefertoExhibit5-9.Theexpecteddailysalesare a.$55,000b.$56,000c.$50,000d.$70,000       .
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    11.Foranycontinuousrandomvariable,theprobabilitythattherandomvariabletakesonexactlyaspecificvalueisa.1.00 b.0.50 c.anyvaluebetween0to1 d.almostzero     12.Forthestandardnormalprobabilitydistribution,theareatotheleftofthemeanisa.-0.5 b.0.5 c.anyvaluebetween0to1 d.1     13.Whichofthefollowingisnotacharacteristicofthenormalprobabilitydistribution? a.Themean,median,andthemodeareequal b.Themeanofthedistributioncanbenegative,zero,orpositive c.Thedistributionissymmetrical d.Thestandarddeviationmustbe1     14.Inastandardnormaldistribution,therangeofvaluesofzisfrom a.minusinfinitytoinfinity b.-1to 1 c.0to 1 d.-3.09to3.09     15.Forauniformprobabilitydensityfunction, a.theheightofthefunctioncannotbelargerthanone b.theheightofthefunctionisthesameforeachvalueofx c.theheightofthefunctionisdifferentforvariousvaluesofx d.theheightofthefunctiondecreasesasxincreases     16.Theprobabilitydensityfunctionforauniformdistributionrangingbetween2and6is a.4 b.undefined c.anypositivevalued.0.25     17.Auniformprobabilitydistributionisacontinuousprobabilitydistributionwheretheprobabilitythattherandomvariableassumesavalueinanyintervalofequallengthis a.differentforeachinterval b.thesameforeachinterval c.atleastone d.Noneofthesealternativesiscorrect.     18.Thefunctionthatdefinestheprobabilitydistributionofacontinuousrandomvariableisa a.normalfunction b.uniformfunction c.eithernormalofuniformdependingonthesituation d.probabilitydensityfunction     19.Whenacontinuousprobabilitydistributionisusedtoapproximateadiscreteprobabilitydistribution a.avalueof0.5isaddedand/orsubtractedfromthearea b.avalueof0.5isaddedand/orsubtractedfromthevalueofx c.avalueof0.5isaddedtothearea d.avalueof0.5issubtractedfromthearea     20.Acontinuousprobabilitydistributionthatisusefulindescribingthetime,orspace,betweenoccurrencesofaneventisa(n) a.normalprobabilitydistribution b.uniformprobabilitydistribution c.exponentialprobabilitydistribution d.Poissonprobabilitydistribution       .
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    71.RefertoExhibit5-9.Theprobabilityofhavingsalesofatleast$50,000isa.0.5 b.0.10 c.0.30 d.0.90       Exhibit5-10 TheprobabilitydistributionforthenumberofgoalstheLionssoccerteammakespergameisgivenbelow.     NumberOfGoals   Probability 00.05 10.15 20.35 30.30 40.15 72.RefertoExhibit5-10.Theexpectednumberofgoalspergameis a.0 b.1 c.2,sinceithasthehighestprobabilityd.2.35     73.RefertoExhibit5-10.WhatistheprobabilitythatinagivengametheLionswillscoreatleast1goal?a.0.20 b.0.55 c.1.0 d.0.95     74.RefertoExhibit5-10.WhatistheprobabilitythatinagivengametheLionswillscorelessthan3goals?a.0.85 b.0.55 c.0.45 d.0.80       75.RefertoExhibit5-10.WhatistheprobabilitythatinagivengametheLionswillscorenogoals?a.0.95 b.0.05 c.0.75 d.0.60       Exhibit5-11 Alocalbottlingcompanyhasdeterminedthenumberofmachinebreakdownspermonthandtheirrespectiveprobabilitiesasshownbelow:     NumberofBreakdowns   Probability 00.12 10.38 20.25 30.18 40.07 76.RefertoExhibit5-11.Theexpectednumberofmachinebreakdownspermonthis a.2 b.1.70 c.one,sinceithasthehighestprobability d.atleast4       77.RefertoExhibit5-11.Theprobabilityofatleast3breakdownsinamonthisa.0.93 b.0.88 c.0.75 d.0.25     78.RefertoExhibit5-11.Theprobabilityofnobreakdownsinamonthisa.0.88 b.0.00 c.0.50 d.0.12         Exhibit5-12   Thepolicerecordsofametropolitanareakeptoverthepast300daysshowthefollowingnumberoffatalaccidents.     NumberofFatalAccidents   NumberofDays 045 175 2120 345 415 79.RefertoExhibit5-12.Whatistheprobabilitythatinagivendaytherewillbelessthan3accidents? a.0.2 b.120 c.0.5 d.0.8       80.RefertoExhibit5-12.Whatistheprobabilitythatinagivendaytherewillbeatleast1accident?a.0.15 b.0.85 c.atleast1d.0.5   81.RefertoExhibit5-12.Whatistheprobabilitythatinagivendaytherewillbenoaccidents?a.0.00 b.1.00 c.0.85 d.0.15         Exhibit5-13 OrientalReproductions,Inc.isacompanythatproduceshandmadecarpetswithorientaldesigns.Theproductionrecordsshowthatthemonthlyproductionhasrangedfrom1to5carpets.Theproductionlevelsandtheirrespectiveprobabilitiesareshownbelow.     ProductionPerMonthx   Probabilityf(x) 10.01 20.04 30.10 40.80 50.05 82.RefertoExhibit5-13.theexpectedmonthlyproductionlevelis a.1.00 b.4.00 c.3.00 d.3.84       83.RefertoExhibit5-13.Thestandarddeviationfortheproductionisa.4.32 b.3.74 c.0.374 d.0.612           .
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  139.Themonthlyearningsofcomputersystemsanalystsarenormallydistributedwithameanof$4,300.Ifonly1.07percentofthesystemsanalystshaveamonthlyincomeofmorethan$6,140,whatisthevalueofthestandarddeviationofthemonthlyearningsofthecomputersystemsanalysts?     140.Amajorcreditcardcompanyhasdeterminedthatitscustomerschargeanaverageof$280permonthontheiraccountswithastandarddeviationof$20.   a.Whatpercentageofthecustomerschargesmorethan$275permonth? b.Whatpercentageofthecustomerschargeslessthan$243permonth? c.Whatpercentageofthecustomerschargesbetween$241and$301.60permonth?   141.Theticketsalesforeventsheldatthenewciviccenterarebelievedtobenormallydistributedwithameanof12,000andastandarddeviationof1,000.   a.Whatistheprobabilityofsellingmorethan10,000tickets? b.Whatistheprobabilityofsellingbetween9,500and11,000tickets? c.Whatistheprobabilityofsellingmorethan13,500tickets?   142.Inanormaldistribution,itisknownthat27.34%ofalltheitemsareincludedfrom100uptothemean,andanother45.99%ofalltheitemsareincludedfromthemeanupto145.Determinethemeanandthestandarddeviationofthedistribution.     143.Therecordsshowthat8%oftheitemsproducedbyamachinedonotmeetthespecifications.Usethenormalapproximationtothebinomialdistributiontoanswerthefollowingquestions.Whatistheprobabilitythatasampleof100unitscontains   a.Fiveormoredefectiveunits? b.Tenorfewerdefectiveunits? c.Elevenorlessdefectiveunits?   144.Approximatethefollowingbinomialprobabilitiesbytheuseofnormalapproximation.   a.P(x≤ 12,n=50,p=0.3) b.P(12≤ x≤ 18,n=50,p=0.3)     .
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MultipleChoice 1.Thecenterofanormalcurveis a.alwaysequaltozero b.isthemeanofthedistribution c.cannotbenegative d.isthestandarddeviation       2.Theprobabilitythatacontinuousrandomvariabletakesanyspecificvalue a.isequaltozero b.isatleast0.5 c.dependsontheprobabilitydensityfunction d.isverycloseto1.0     3.Anormaldistributionwithameanof0andastandarddeviationof1iscalled a.aprobabilitydensityfunction b.anordinarynormalcurve c.astandardnormaldistribution d.noneofthesealternativesiscorrect     4.Thezscoreforthestandardnormaldistribution a.isalwaysequaltozero b.canneverbenegative c.canbeeithernegativeorpositive d.isalwaysequaltothemean     5.Inastandardnormaldistribution,theprobabilitythatZisgreaterthanzeroisa.0.5 b.equalto1 c.atleast0.5d.1.96       6.AnegativevalueofZindicatesthat a.thenumberofstandarddeviationsofanobservationistotherightofthemean b.thenumberofstandarddeviationsofanobservationistotheleftofthemean c.amistakehasbeenmadeincomputations,sinceZcannotbenegative d.thedatahasanegativemean     7.Theuniform,normal,andexponentialdistributionsare a.allcontinuousprobabilitydistributions b.alldiscreteprobabilitydistributions c.canbeeithercontinuousordiscrete,dependingonthedata d.allthesamedistributions     8.Avalueof0.5thatisaddedand/orsubtractedfromavalueofxwhenthecontinuousnormaldistributionisusedtoapproximatethediscretebinomialdistributioniscalled a.50%oftheareaunderthenormalcurve b.continuitycorrectionfactor c.factorofconversion d.allofthealternativesarecorrectanswers     9.Foracontinuousrandomvariablex,theprobabilitydensityfunctionf(x)represents a.theprobabilityatagivenvalueofx b.theareaunderthecurveatx c.theareaunderthecurvetotherightofx d.theheightofthefunctionatx     10.Theuniformprobabilitydistributionisusedwith a.acontinuousrandomvariable b.adiscreterandomvariable c.anormallydistributedrandomvariable d.anyrandomvariable,aslongasitisnotnominal           .
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    11.Fromagroupofsixpeople,twoindividualsaretobeselectedatrandom.Howmanypossibleselectionsarethere? a.12 b.36 c.15 d.8     12.Whentheresultsofexperimentationorhistoricaldataareusedtoassignprobabilityvalues,themethodusedtoassignprobabilitiesisreferredtoasthe a.relativefrequencymethod b.subjectivemethod c.classicalmethod d.posteriormethod     13.Amethodofassigningprobabilitiesbaseduponjudgmentisreferredtoasthe a.relativemethod b.probabilitymethod c.classicalmethod d.subjectivemethod     14.Asamplepointreferstothe a.numericalmeasureofthelikelihoodoftheoccurrenceofanevent b.setofallpossibleexperimentaloutcomes c.individualoutcomeofanexperiment d.samplespace     15.Agraphicaldeviceusedforenumeratingsamplepointsinamultiple-stepexperimentisa a.barchart b.piechart c.histogram d.Noneofthesealternativesiscorrect.       16.Theintersectionoftwomutuallyexclusiveevents a.canbeanyvaluebetween0to1 b.mustalwaysbeequalto1 c.mustalwaysbeequalto0 d.canbeanypositivevalue     17.Twoeventsaremutuallyexclusive a.iftheirintersectionis1 b.iftheyhavenosamplepointsincommon c.iftheirintersectionis0.5 d.Noneofthesealternativesiscorrect.     18.Therangeofprobabilityis a.anyvaluelargerthanzero b.anyvaluebetweenminusinfinitytoplusinfinity c.zerotoone d.anyvaluebetween-1to1     19.Whichofthefollowingstatementsisalwaystrue? a.-1≤P(Ei)≤1 b.P(A)=1-(Ac) c.P(A)+P(B)=1 d.∑P≥1     20.Eventsthathavenosamplepointsincommonare a.independentevents b.posteriorevents c.mutuallyexclusiveevents d.complements       .
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  100.Arandomvariablexhasthefollowingprobabilitydistribution:     xf(x) 00.08 10.17 20.45 30.25 40.05     a.Determinetheexpectedvalueofx. b.Determinethevariance.       101.Acompanysellsitsproductstowholesalersinbatchesof1,000unitsonly.Thedailydemandforitsproductandtherespectiveprobabilitiesaregivenbelow.     Demand(Units)Probability 00.2 10000.2 20000.3 30000.2 40000.1     a.Determinetheexpecteddailydemand. b.Assumethatthecompanysellsitsproductat$3.75perunit.Whatistheexpecteddailyrevenue?     102.Therecordsofadepartmentstoreshowthat20%ofitscustomerswhomakeapurchasereturnthemerchandiseinordertoexchangeit.Inthenextsixpurchases,   a.whatistheprobabilitythatthreecustomerswillreturnthemerchandiseforexchange? b.whatistheprobabilitythatfourcustomerswillreturnthemerchandiseforexchange? c.whatistheprobabilitythatnoneofthecustomerswillreturnthemerchandiseforexchange?   103.Inalargeuniversity,15%ofthestudentsarefemale.Ifarandomsampleoftwentystudentsisselected,   a.whatistheprobabilitythatthesamplecontainsexactlyfourfemalestudents? b.whatistheprobabilitythatthesamplewillcontainnofemalestudents? c.whatistheprobabilitythatthesamplewillcontainexactlytwentyfemalestudents? d.whatistheprobabilitythatthesamplewillcontainmorethanninefemalestudents? e.whatistheprobabilitythatthesamplewillcontainfewerthanfivefemalestudents? f.whatistheexpectednumberoffemalestudents?       104.Inasouthernstate,itwasrevealedthat5%ofallautomobilesinthestatedidnotpassinspection.Ofthenexttenautomobilesenteringtheinspectionstation,   a.whatistheprobabilitythatnonewillpassinspection? b.whatistheprobabilitythatallwillpassinspection? c.whatistheprobabilitythatexactlytwowillnotpassinspection? d.whatistheprobabilitythatmorethanthreewillnotpassinspection? e.whatistheprobabilitythatfewerthantwowillnotpassinspection? f.Findtheexpectednumberofautomobilesnotpassinginspection. g.Determinethestandarddeviationforthenumberofcarsnotpassinginspection.       .
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    21.Theexponentialprobabilitydistributionisusedwith a.adiscreterandomvariable b.acontinuousrandomvariable c.anyprobabilitydistributionwithanexponentialterm d.anapproximationofthebinomialprobabilitydistribution         22.Inastandardnormaldistributiontheprobabilityofzbeinglessthanorequalzeroisa.0.0000 b.muchlargerthan1 c.thereisnoanswertothisquestion,sincethevalueofthemeanisnotknownd.0.5000   23.Largervaluesofthestandarddeviationresultinanormalcurvethatis a.shiftedtotheright b.shiftedtotheleft c.narrowerandmorepeaked d.widerandflatter     24.Whichofthefollowingisnotacharacteristicofthenormalprobabilitydistribution? a.symmetry b.Thetotalareaunderthecurveisalwaysequalto1. c.99.72%ofthetimetherandomvariableassumesavaluewithinplusorminus1standarddeviationofitsmean d.Themeanisequaltothemedian,whichisalsoequaltothemode.     25.Foranormaldistribution,anegativevalueofzindicates a.amistakehasbeenmadeincomputations,becausezisalwayspositive b.theareacorrespondingtothezisnegative c.thezistotheleftofthemean d.thezistotherightofthemean     26.Themeanofastandardnormalprobabilitydistribution a.isalwaysequaltozero b.canbeanyvalueaslongasitispositive c.canbeanyvalue d.isalwaysgreaterthanzero         27.Thestandarddeviationofastandardnormaldistribution a.isalwaysequaltozero b.isalwaysequaltoone c.canbeanypositivevalue d.canbeanyvalue     28.Anormalprobabilitydistribution a.isacontinuousprobabilitydistribution b.isadiscreteprobabilitydistribution c.canbeeithercontinuousordiscrete d.musthaveastandarddeviationof1     29.Acontinuousrandomvariablemayassume a.allvaluesinanintervalorcollectionofintervals b.onlyintegervaluesinanintervalorcollectionofintervals c.onlyfractionalvaluesinanintervalorcollectionofintervals d.allthepositiveintegervaluesinaninterval     30.Acontinuousrandomvariableisuniformlydistributedbetweenaandb.Theprobabilitydensityfunctionbetweenaandb is a.zero b.(a-b) c.(b-a)d.1/(b-a)     .
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    61.Theentireareaunderthestandardnormaldistributioncurve a.canbeanyvalue b.cannotbenegative c.canbeanypositivevalue d.canbeanypositivevaluelargerthan1     62.Zisastandardnormalrandomvariable.TheP(-1.5≤ Z≤ 1.09)equalsa.0.4322 b.0.3621 c.0.7953 d.0.0711         63.GiventhatZisastandardnormalrandomvariable.WhatisthevalueofZiftheareatotheleftofZis0.9382?a.1.8 b.1.54 c.2.1 d.1.77     64.GiventhatZisastandardnormalrandomvariable.WhatisthevalueofZiftheareatotherightofZis0.1401?a.1.08 b.0.1401 c.2.16 d.-1.08     65.GiventhatZisastandardnormalrandomvariable.WhatisthevalueofZiftheareabetween-ZandZis0.754? a.1.16 b.1.96 c.2.0 d.11.6   66.GiventhatZisastandardnormalrandomvariable,whatisthevalueofZiftheareatotherightofZis0.9834?a.0.4834 b.-2.13 c.+2.13 d.zero     67.GiventhatZisastandardnormalrandomvariable,whatisthevalueofZiftheareatotheleftofZis0.119?a.0.381 b.+1.18 c.-1.18 d.2.36     68.GiventhatZisastandardnormalrandomvariable,whatisthevalueofZiftheareabetween-ZandZis0.901?a.1.96 b.-1.96 c.0.4505 d.±1.65       69.Inastandardnormaldistributionthevalueofz a.canbeanyvalue b.cannotbenegative c.cannotbelargerthan3.09 d.cannotbelargerthan0.50     Exhibit6-1 Theassemblytimeforaproductisuniformlydistributedbetween6to10minutes. 70.RefertoExhibit6-1.Theprobabilitydensityfunctionhaswhatvalueintheintervalbetween6and10?a.0.25 b.4.00 c.5.00 d.zero         .
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    51.Ifacoinistossedthreetimes,thelikelihoodofobtainingthreeheadsinarowis a.zerob.0.500c.0.875d.0.125   52.Theunionoftwoeventswithnonzeroprobabilities a.cannotbelessthanone b.cannotbeone c.couldbelargerthanone d.Noneofthesealternativesiscorrect.       53.IfP(A)=0.5andP(B)=0.5,thenP(A∩B) a.is0.00 b.is1.00 c.is0.5 d.Noneofthesealternativesiscorrect.     54.IfAandBareindependenteventswithP(A)=0.4andP(B)=0.6,thenP(A∩B)=a.0.76 b.1.00 c.0.24 d.0.20   55.IfAandBareindependenteventswithP(A)=0.2andP(B)=0.6,thenP(A∪B)=a.0.62 b.0.12 c.0.60 d.0.68       56.IfAandBareindependenteventswithP(A)=0.05andP(B)=0.65,thenP(A|B)=a.0.05 b.0.0325 c.0.65 d.0.8     57.IfAandBaremutuallyexclusiveeventswithP(A)=0.3andP(B)=0.5,thenP(A∩B)=a.0.30 b.0.15 c.0.00 d.0.20   58.IfAandBaremutuallyexclusiveeventswithP(A)=0.4andP(B)=0.45,thenP(A∪B)=a.0.00 b.0.15 c.0.95 d.0.2       59.Alotteryisconductedusingthreeurns.Eachurncontainschipsnumberedfrom0to9.Onechipisselectedatrandomfromeachurn.Thetotalnumberofsamplepointsinthesamplespaceis a.30b.100c.729 d.1,000     60.Ofthelast100customersenteringacomputershop,25havepurchasedacomputer.Iftheclassicalmethodforcomputingprobabilityisused,theprobabilitythatthenextcustomerwillpurchaseacomputeris a.0.25 b.0.50 c.1.00 d.0.75         .
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  89.Asalespersoncontactseightpotentialcustomersperday.Frompastexperience,weknowthattheprobabilityofapotentialcustomermakingapurchaseis.10.   a.Whatistheprobabilitythesalespersonwillmakeexactlytwosalesinaday? b.Whatistheprobabilitythesalespersonwillmakeatleasttwosalesinaday? c.Whatpercentageofdayswillthesalespersonnotmakeasale? d.Whatistheexpectednumberofsalesperday? 90.AlifeinsurancecompanyhasdeterminedthateachweekanaverageofsevenclaimsisfiledinitsNashvillebranch.   a.Whatistheprobabilitythatduringthenextweekexactlysevenclaimswillbefiled? b.Whatistheprobabilitythatduringthenextweeknoclaimswillbefiled? c.Whatistheprobabilitythatduringthenextweekfewerthanfourclaimswillbefiled? d.Whatistheprobabilitythatduringthenextweekatleastseventeenclaimswillbefiled?   91.Whenaparticularmachineisfunctioningproperly,80%oftheitemsproducedarenon-defective.Ifthreeitemsareexamined,whatistheprobabilitythatoneisdefective?Usethebinomialprobabilityfunctiontoanswerthisquestion.       92.Tenpercentoftheitemsproducedbyamachinearedefective.Outof15itemschosenatrandom,   a.whatistheprobabilitythatexactly3itemswillbedefective? b.whatistheprobabilitythatlessthan3itemswillbedefective? c.whatistheprobabilitythatexactly11itemswillbenon-defective?   93.Thestudentbodyofalargeuniversityconsistsof30%Businessmajors.Arandomsampleof20studentsisselected.   a.Whatistheprobabilitythatamongthestudentsinthesampleatleast10areBusinessmajors? b.Whatistheprobabilitythatatleast16arenotBusinessmajors? c.Whatistheprobabilitythatexactly10areBusinessmajors? d.Whatistheprobabilitythatexactly12arenotBusinessmajors?   94.ShoppersenterHamiltonPlaceMallatanaverageof120perhour.   a.0.0378 b.0.0015       .
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  SubjectiveShortAnswer 84.Thirty-twopercentofthestudentsinamanagementclassaregraduatestudents.Arandomsampleof5studentsisselected.Usingthebinomialprobabilityfunction,determinetheprobabilitythatthesamplecontainsexactly2graduatestudents?       85.Seventypercentofthestudentsapplyingtoauniversityareaccepted.Usingthebinomialprobabilitytables,whatistheprobabilitythatamongthenext18applicants   a.Atleast6willbeaccepted? b.Exactly10willbeaccepted? c.Exactly5willberejected? d.Fifteenormorewillbeaccepted? e.Determinetheexpectednumberofacceptances. f.Computethestandarddeviation.   86.GeneralHospitalhasnotedthattheyadmitanaverageof8patientsperhour.   a.Whatistheprobabilitythatduringthenexthourlessthen3patientswillbeadmitted? b.Whatistheprobabilitythatduringthenexttwohoursexactly8patientswillbeadmitted? 87.Thedemandforaproductvariesfrommonthtomonth.Basedonthepastyear'sdata,thefollowingprobabilitydistributionshowsMNMcompany'smonthlydemand.     x UnitDemandf(x)Probability 00.10 1,0000.10 2,0000.30 3,0000.40 4,0000.10     a.Determinetheexpectednumberofunitsdemandedpermonth. b.Eachunitproducedcoststhecompany$8.00,andissoldfor$10.00.Howmuchwillthecompanygainorloseinamonthiftheystocktheexpectednumberofunitsdemanded,butsell2000units?           88.Twenty-fivepercentoftheemployeesofalargecompanyareminorities.Arandomsampleof7employeesisselected.   a.Whatistheprobabilitythatthesamplecontainsexactly4minorities? b.Whatistheprobabilitythatthesamplecontainsfewerthan2minorities? c.Whatistheprobabilitythatthesamplecontainsexactly1non-minority? d.Whatistheexpectednumberofminoritiesinthesample? e.Whatisthevarianceoftheminorities?       .
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    11.Thevarianceisameasureofdispersionorvariabilityofarandomvariable.Itisaweightedaverageofthe a.squarerootofthedeviationsfromthemean b.squarerootofthedeviationsfromthemedian c.squareddeviationsfromthemedian d.squareddeviationsfromthemean       12.Aweightedaverageofthevalueofarandomvariable,wheretheprobabilityfunctionprovidesweightsisknownas a.aprobabilityfunction b.arandomvariable c.theexpectedvalue d.randomfunction     13.Anexperimentconsistsofmaking80telephonecallsinordertosellaparticularinsurancepolicy.Therandomvariableinthisexperimentisa a.discreterandomvariable b.continuousrandomvariable c.complexrandomvariable d.simplexrandomvariable     14.Anexperimentconsistsofdeterminingthespeedofautomobilesonahighwaybytheuseofradarequipment.Therandomvariableinthisexperimentisa a.discreterandomvariable b.continuousrandomvariable c.complexrandomvariable d.simplexrandomvariable     15.Thenumberofelectricaloutagesinacityvariesfromdaytoday.Assumethatthenumberofelectricaloutages(x)inthecityhasthefollowingprobabilitydistribution.   xf(x) 00.80 10.15 20.04 30.01   Themeanandthestandarddeviationforthenumberofelectricaloutages(respectively)area.2.6and5.77 b.0.26and0.577 c.3and0.01 d.0and0.8         16.Thenumberofcustomersthatenterastoreduringonedayisanexampleof a.acontinuousrandomvariable b.adiscreterandomvariable c.eitheracontinuousoradiscreterandomvariable,dependingonthenumberofthecustomers d.eitheracontinuousoradiscreterandomvariable,dependingonthegenderofthecustomers     17.Theweightofanobjectisanexampleof a.acontinuousrandomvariable b.adiscreterandomvariable c.eitheracontinuousoradiscreterandomvariable,dependingontheweightoftheobject d.eitheracontinuousoradiscreterandomvariabledependingontheunitsofmeasurement     18.Fourpercentofthecustomersofamortgagecompanydefaultontheirpayments.Asampleoffivecustomersisselected.Whatistheprobabilitythatexactlytwocustomersinthesamplewilldefaultontheirpayments? a.0.2592 b.0.0142 c.0.9588 d.0.7408     19.Whensamplingwithoutreplacement,theprobabilityofobtainingacertainsampleisbestgivenbya a.hypergeometricdistribution b.binomialdistribution c.Poissondistribution d.normaldistribution     20.Twentypercentofthestudentsinaclassof100areplanningtogotograduateschool.Thestandarddeviationofthisbinomialdistributionis a.20 b.16 c.4 d.2           .
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    31.Ifthemeanofanormaldistributionisnegative, a.thestandarddeviationmustalsobenegative b.thevariancemustalsobenegative c.amistakehasbeenmadeinthecomputations,becausethemeanofanormaldistributioncannotbenegative d.Noneofthesealternativesiscorrect.         32.Forastandardnormaldistribution,theprobabilityofz≤ 0is a.zerob.-0.5c.0.5 d.one     33.Thehighestpointofanormalcurveoccursat a.onestandarddeviationtotherightofthemean b.twostandarddeviationstotherightofthemean c.approximatelythreestandarddeviationstotherightofthemean d.themean     34.Therandomvariablexisknowntobeuniformlydistributedbetween70and90.Theprobabilityofxhavingavaluebetween80to95is a.0.75 b.0.5 c.0.05 d.1     35.Zisastandardnormalrandomvariable.TheP(-1.96≤Z≤-1.4)equalsa.0.8942 b.0.0558 c.0.475 d.0.4192     36.Astandardnormaldistributionisanormaldistribution a.withameanof1andastandarddeviationof0 b.withameanof0andastandarddeviationof1 c.withanymeanandastandarddeviationof1 d.withanymeanandanystandarddeviation         37.Zisastandardnormalrandomvariable.TheP(1.20≤ Z≤1.85)equalsa.0.4678 b.0.3849 c.0.8527 d.0.0829     38.Zisastandardnormalrandomvariable.TheP(-1.20≤ Z≤ 1.50)equalsa.0.0483 b.0.3849 c.0.4332 d.0.8181     39.GiventhatZisastandardnormalrandomvariable,whatistheprobabilitythat-2.51≤ Z≤-1.53?a.0.4950 b.0.4370 c.0.0570 d.0.9310     40.GiventhatZisastandardnormalrandomvariable,whatistheprobabilitythatZ≥ -2.12?a.0.4830 b.0.9830 c.0.017 d.0.966       .
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    81.Thefollowingdatawascollectedfromasimplerandomsampleofapopulation.1315141612 Thepointestimateofthepopulationstandarddeviationisa.2.500 b.1.581 c.2.000 d.1.414     82.Thefollowingdatawascollectedfromasimplerandomsampleofapopulation.1315141612 Ifthepopulationconsistedof10elements,howmanydifferentrandomsamplesofsize6couldbedrawnfromthepopulation? a.60b.210 c.3024 d.362880       83.Thefollowingdatawascollectedfromasimplerandomsampleofapopulation.1315141612 Themeanofthepopulation a.is14 b.is15 c.is15.1581 d.couldbeanyvalue     84.Fourhundredpeoplewereaskedwhethergunlawsshouldbemorestringent.Threehundredsaid"yes,"and100said"no."Thepointestimateoftheproportioninthepopulationwhowillrespond"yes"is a.300 b.approximately300c.0.75 d.0.25       85.Fourhundredpeoplewereaskedwhethergunlawsshouldbemorestringent.Threehundredsaid"yes,"and100said"no."Thepointestimateoftheproportioninthepopulationwhowillrespond"no"is a.75b.0.25c.0.75d.0.50 86.Thefollowinginformationwascollectedfromasimplerandomsampleofapopulation.161918172018 Thepointestimateofthemeanofthepopulationisa.18.0 b.19.6 c.108 d.sixteen,since16isthesmallestvalueinthesample       87.Thefollowinginformationwascollectedfromasimplerandomsampleofapopulation.161918172018 Thepointestimateofthepopulationstandarddeviationisa.2.000 b.1.291 c.1.414 d.1.667     88.Howmanydifferentsamplesofsize3canbetakenfromafinitepopulationofsize10? a.30 b.1,000 c.720 d.120       89.Thesamplingerroristhe a.sameasthestandarderrorofthemean b.differencebetweenthevalueofthesamplemeanandthevalueofthesampleproportion c.errorcausedbyselectingabadsample d.absolutevalueofthedifferencebetweentheproportionofthepopulationandproportionofthesample     Exhibit7-1 Arandomsampleof121bottlesofcologneshowedanaveragecontentof4ounces.Itisknownthatthestandarddeviationofthecontents(i.e.,ofthepopulation)is0.22ounces. 90.RefertoExhibit7-1.Thestandarderrorofthemeanequalsa.0.3636 b.0.0331 c.0.0200 d.4.000         .
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  110.Ontheaverage,6.7carsarriveatthedrive-upwindowofabankeveryhour.DefinetherandomvariableXtobethenumberofcarsarrivinginanyhour.     a.WhatistheappropriateprobabilitydistributionforX?ExplainhowXsatisfiesthepropertiesofthedistribution. b.Computetheprobabilitythatexactly5carswillarriveinthenexthour. c.Computetheprobabilitythatnomorethan5carswillarriveinthenexthour.     111.Twenty-fivepercentofallresumesreceivedbyacorporationforamanagementpositionarefromfemales.Fifteenresumeswillbereceivedtomorrow.   a.Whatistheprobabilitythatexactly5oftheresumeswillbefromfemales? b.Whatistheprobabilitythatfewerthan3oftheresumeswillbefromfemales? c.Whatistheexpectednumberofresumesfromwomen? d.Whatisthevarianceofthenumberofresumesfromwomen?     112.Theaveragenumberofcallsreceivedbyaswitchboardina30-minuteperiodis15.     a.Whatistheprobabilitythatbetween10:00and10:30theswitchboardwillreceiveexactly10calls? b.Whatistheprobabilitythatbetween10:00and10:30theswitchboardwillreceivemorethan9callsbutfewerthan15calls? c.Whatistheprobabilitythatbetween10:00and10:30theswitchboardwillreceivefewerthan7calls?   113.Twopercentofthepartsproducedbyamachinearedefective.Twentypartsareselectedatrandom.Usethebinomialprobabilitytablestoanswerthefollowingquestions.   a.Whatistheprobabilitythatexactly3partswillbedefective? b.Whatistheprobabilitythatthenumberofdefectivepartswillbemorethan2butfewerthan6? c.Whatistheprobabilitythatfewerthan4partswillbedefective? d.Whatistheexpectednumberofdefectiveparts? e.Whatisthevarianceforthenumberofdefectiveparts?     114.Computethehypergeometricprobabilitiesforthefollowingvaluesofnandx.AssumeN=8andr=5.   a.n=5,x=2b.n=6,x=4c.n=3,x=0d.n=3,x=3       .
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    61.EventsAandBaremutuallyexclusivewithP(A)=0.3andP(B)=0.2.Then,P(Bc)=a.0.00 b.0.06 c.0.7 d.0.8     62.AnexperimentconsistsoffouroutcomeswithP(E1)=0.2,P(E2)=0.3,andP(E3)=0.4.TheprobabilityofoutcomeE4is a.0.500 b.0.024 c.0.100 d.0.900     63.EventsAandBaremutuallyexclusive.Whichofthefollowingstatementsisalsotrue? a.AandBarealsoindependent. b.P(A∪B)=P(A)P(B) c.P(A∪B)=P(A)+P(B) d.P(A∩B)=P(A)+P(B)       64.Asix-sideddieistossed3times.Theprobabilityofobservingthreeonesinarowisa.1/3 b.1/6c.1/27d.1/216   65.TheprobabilityoftheoccurrenceofeventAinanexperimentis1/3.Iftheexperimentisperformed2timesandeventAdidnotoccur,thenonthethirdtrialeventA a.mustoccur b.mayoccur c.couldnotoccur d.hasa2/3probabilityofoccurring       66.Aperfectlybalancedcoinistossed6timesandtailsappearsonallsixtosses.Then,ontheseventhtrial a.tailscannotappear b.headshasalargerchanceofappearingthantails c.tailshasabetterchanceofappearingthanheads d.Noneofthesealternativesiscorrect.     67.Inanexperiment,eventsAandBaremutuallyexclusive.IfP(A)=0.6,thentheprobabilityofB a.cannotbelargerthan0.4 b.canbeanyvaluegreaterthan0.6 c.canbeanyvaluebetween0to1 d.cannotbedeterminedwiththeinformationgiven     68.Thesetofallpossiblesamplepoints(experimentaloutcomes)iscalled a.asample b.anevent c.thesamplespace d.apopulation       69.Amethodofassigningprobabilitieswhichassumesthattheexperimentaloutcomesareequallylikelyisreferredtoasthe a.objectivemethod b.classicalmethod c.subjectivemethod d.experimentalmethod     70.Amethodofassigningprobabilitiesbasedonhistoricaldataiscalledthe a.classicalmethod b.subjectivemethod c.relativefrequencymethod d.historicalmethod       .
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  145.AssumethateachyeartheIRSrandomlyaudits10%ofthetaxreturns.Ifamarriedcouplehasfiledseparatereturns,   a.Whatistheprobabilitythatboththehusbandandthewifewillbeaudited? b.Whatistheprobabilitythatonlyoneofthemwillbeaudited? c.Whatistheprobabilitythatneitheroneofthemwillbeaudited? d.Whatistheprobabilitythatatleastoneofthemwillbeaudited?   146.Tammyisageneralcontractorandhassubmittedtwobidsfortwoprojects(AandB).TheprobabilityofgettingprojectAis0.65.TheprobabilityofgettingprojectBis0.77.Theprobabilityofgettingatleastoneoftheprojectsis0.90.     a.Whatistheprobabilitythatshewillgetbothprojects? b.Aretheeventsofgettingthetwoprojectsmutuallyexclusive?Explain,usingprobabilities. c.Arethetwoeventsindependent?Explain,usingprobabilities. 147.Assumeyouaretakingtwocoursesthissemester(AandB).TheprobabilitythatyouwillpasscourseAis0.835,theprobabilitythatyouwillpassbothcoursesis0.276.Theprobabilitythatyouwillpassatleastoneofthecoursesis0.981.     a.WhatistheprobabilitythatyouwillpasscourseB? b.Isthepassingofthetwocoursesindependentevents?Useprobabilityinformationtojustifyyouranswer. c.Aretheeventsofpassingthecoursesmutuallyexclusive?Explain.     148.InarandomsampleofUTCstudents50%indicatedtheyarebusinessmajors,40%engineeringmajors,and10%othermajors.Ofthebusinessmajors,60%werefemales;whereas,30%ofengineeringmajorswerefemales.Finally,20%oftheothermajorswerefemale.   a.Whatpercentageofstudentsinthissamplewasfemale? b.Giventhatapersonisfemale,whatistheprobabilitythatsheisanengineeringmajor? 149.InarecentsurveyinaStatisticsclass,itwasdeterminedthatonly60%ofthestudentsattendclassonFridays.Frompastdataitwasnotedthat98%ofthosewhowenttoclassonFridayspassthecourse,whileonly20%ofthosewhodidnotgotoclassonFridayspassedthecourse.   a.Whatpercentageofstudentsisexpectedtopassthecourse? b.Giventhatapersonpassesthecourse,whatistheprobabilitythathe/sheattendedclassesonFridays?     150.YouareapplyingforgraduateschoolatUniversityA.Inthepast42%oftheapplicantstothisuniversityhavebeenaccepted.Itisalsoknownthat70%ofthosestudentswhohavebeenacceptedhavehadGMATscoresinexcessof550while40%ofthestudentswhowerenotacceptedhadGMATscoresinexcessof550.YoutaketheGMATexamandscore640.WhatistheprobabilitythatyouwillbeacceptedintograduateschoolofuniversityA?   151.Inarecentsurveyaboutapplianceownership,58.3%oftherespondentsindicatedthattheyownMaytagappliances,while23.9%indicatedtheyownbothMaytagandGEappliancesand70.7%saidtheyownatleastoneofthetwoappliances.   Definetheeventsas M=OwningaMaytagapplianceG=OwningaGEappliance     a.WhatistheprobabilitythatarespondentownsaGEappliance? b.GiventhatarespondentownsaMaytagappliance,whatistheprobabilitythattherespondentalsoownsaGEappliance? c.Areevents"M"and"G"mutuallyexclusive?Whyorwhynot?Explain,usingprobabilities. d.Arethetwoevents"M"and"G"independent?Explain,usingprobabilities.   152.Recordsofacompanyshowthat20%oftheemployeeshaveonlyahighschooldiploma;70%havebachelordegrees;and10%havegraduatedegrees.Ofthosewithonlyahighschooldiploma,10%holdmanagementpositions;whereas,ofthosehavingbachelordegrees,40%holdmanagementpositions.Finally,80%oftheemployeeswhohavegraduatedegreesholdmanagementpositions.   a.Whatpercentageofemployeesholdsmanagementpositions? b.Giventhatapersonholdsamanagementposition,whatistheprobabilitythatshe/hehasagraduatedegree?       .
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  SubjectiveShortAnswer 100.Apopulationof1,000studentsspendsanaverageof$10.50adayondinner.Thestandarddeviationoftheexpenditureis$3.Asimplerandomsampleof64studentsistaken.     a.Whataretheexpectedvalue,standarddeviation,andshapeofthesamplingdistributionofthesamplemean? b.Whatistheprobabilitythatthese64studentswillspendacombinedtotalofmorethan$715.21? c.Whatistheprobabilitythatthese64studentswillspendacombinedtotalbetween$703.59and $728.45?     101.Asimplerandomsampleof6recentgraduatesrevealedthefollowinginformationabouttheirweeklyincomes.     GraduatesWeeklyIncome A$250 B270 C285 D240 E255 F290     a.Whatistheexpectedvalueoftheaverageweeklyincomeofalltherecentgraduates? b.Whatistheexpectedvalueofthestandarddeviationforthepopulation?   102.ThelifeexpectancyintheUnitedStatesis75withastandarddeviationof7years.Arandomsampleof49individualsisselected.   a.Whatistheprobabilitythatthesamplemeanwillbelargerthan77years? b.Whatistheprobabilitythatthesamplemeanwillbelessthan72.7years? c.Whatistheprobabilitythatthesamplemeanwillbebetween73.5and76years? d.Whatistheprobabilitythatthesamplemeanwillbebetween72and74years? e.Whatistheprobabilitythatthesamplemeanwillbelargerthan73.46years?       103.TheSATscoreshaveanaverageof1200withastandarddeviationof60.Asampleof36scoresisselected.   a.Whatistheprobabilitythatthesamplemeanwillbelargerthan1224? b.Whatistheprobabilitythatthesamplemeanwillbelessthan1230? c.Whatistheprobabilitythatthesamplemeanwillbebetween1200and1214? d.Whatistheprobabilitythatthesamplemeanwillbegreaterthan1200? e.Whatistheprobabilitythatthesamplemeanwillbelargerthan73.46?   104.Asimplerandomsampleof8employeesofacorporationprovidedthefollowinginformation.   Employee12345678 Age2532264050542223 GenderMMMMFMMF   a.Determinethepointestimatefortheaverageageofallemployees. b.Whatisthepointestimateforthestandarddeviationofthepopulation? c.Determineapointestimatefortheproportionofallemployeeswhoarefemale.         .
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