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Question : According to a recent study, 1 in every 7 women has been a victim of domestic abuse : 2150448

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Solve the problem.**

62) According to a recent study, 1 in every 7 women has been a victim of domestic abuse at some point in her life. Suppose we have randomly and independently sampled twenty-five women and asked each whether she has been a victim of domestic abuse at some point in her life. Find the probability that at least 2 of the women sampled have been the victim of domestic abuse. Round to six decimal places.

A) 0.713804

B) 0.109532

C) 0.176664

D) 0.890468

64) We believe that 94% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 38 students from the population and observed fewer than five in our sample who consider statistics to be an exciting subject. Make an inference about the belief that 94% of the students consider statistics to be an exciting subject.

A) The 94% number is too high. The real percentage is lower than 94%.

B) The 94% number is exactly right.

C) The 94% number is too low. The real percentage is higher than 94%.

D) It is impossible to make any inferences about the 94% number based on this information.

65) We believe that 77% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 24 students from the population. If the true percentage is really 77%, find the probability of observing 23 or more students who consider statistics to be an exciting subject. Round to six decimal places.

A) 0.001887

B) 0.015415

C) 0.984585

D) 0.013528

66) A literature professor decides to give a 10-question true-false quiz. She wants to choose the passing grade such that the probability of passing a student who guesses on every question is less than .10. What score should be set as the lowest passing grade?

A) 9

B) 8

C) 7

D) 6

67) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 44% of all employees believe their company president possesses low ethical standards. Assume that responses were randomly and independently collected. A president of a local company that employs 1,000 people does not believe the paper's claim applies to her company. If the claim is true, how many of her company's employees believe that she possesses low ethical standards?

A) 44

B) 560

C) 956

D) 440

68) A recent article in the paper claims that business ethics are at an all-time low. Reporting on a recent sample, the paper claims that 37% of all employees believe their company president possesses low ethical standards. Suppose 20 of a company's employees are randomly and independently sampled. Assuming the paper's claim is correct, find the probability that more than eight but fewer than 12 of the 20 sampled believe the company's president possesses low ethical standards. Round to six decimal places.

A) 0.269668

B) 0.182165

C) 0.378753

D) 0.462968

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

76) If x* *is a binomial random variable, calculate μ for n = 25 and p = 0.3.

A) 12.5

B) 0.75

C) 5.25

D) 7.5

77) If x* *is a binomial random variable, calculate σ^{2} for n = 75 and p = 0.4.

A) 30

B) 12

C) 18

D) 4.243

78) If x* *is a binomial random variable, calculate σ for n = 50 and p = 0.8. Round to three decimal places when necessary.

A) 2.828

B) 6.325

C) 8

D) 40

79) The probability that an individual is left-handed is 0.15. In a class of 60 students, what is the mean and standard deviation of the number of left-handed students? Round to the nearest hundredth when necessary.

A) mean: 9; standard deviation: 3

B) mean: 9; standard deviation: 2.77

C) mean: 60; standard deviation: 3

D) mean: 60; standard deviation: 2.77

80) A recent survey found that 70% of all adults over 50 wear glasses for driving. In a random sample of 40 adults over 50, what is the mean and standard deviation of the number who wear glasses? Round to the nearest hundredth when necessary.

A) mean: 12; standard deviation: 5.29

B) mean: 28; standard deviation: 2.9

C) mean: 28; standard deviation: 5.29

D) mean: 12; standard deviation: 2.9

81) According to a published study, 1 in every 10 men has been involved in a minor traffic accident. Suppose we have randomly and independently sampled twenty-five men and asked each whether he has been involved in a minor traffic accident. How many of the 25 men do we expect to have never been involved in a minor traffic accident? Round to the nearest whole number.

A) 10

B) 25

C) 22

D) 3

82) We believe that 81% of the population of all Business Statistics students consider statistics to be an exciting subject. Suppose we randomly and independently selected 39 students from the population. How many of the sampled students do we expect to consider statistics to be an exciting subject?

A) 39

B) 32.16

C) 33.82

D) 31.59

**Solve the problem.**

103) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 50 seconds. Find the probability that a randomly selected boy in secondary school can run the mile in less than 345 seconds.

A) .4893

B) .0107

C) .5107

D) .9893

104) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 460 seconds and a standard deviation of 40 seconds. The fitness association wants to recognize the fastest 10% of the boys with certificates of recognition. What time would the boys need to beat in order to earn a certificate of recognition from the fitness association?

A) 394.2 seconds

B) 408.8 seconds

C) 525.8 seconds

D) 511.2 seconds

105) A physical fitness association is including the mile run in its secondary-school fitness test. The time for this event for boys in secondary school is known to possess a normal distribution with a mean of 440 seconds and a standard deviation of 60 seconds. Between what times do we expect approximately 95% of the boys to run the mile?

A) between 345 and 535 seconds

B) between 0 and 538.736 seconds

C) between 322.4 and 557.6 seconds

D) between 341.3 and 538.736 seconds

109) The amount of soda a dispensing machine pours into a 12-ounce can of soda follows a normal distribution with a standard deviation of 0.24 ounce. Every can that has more than 12.60 ounces of soda poured into it causes a spill and the can must go through a special cleaning process before it can be sold. What is the mean amount of soda the machine should dispense if the company wants to limit the percentage that must be cleaned because of spillage to 3%?

A) 12.1488 ounces

B) 12.0792 ounces

C) 13.0512 ounces

D) 13.1208 ounces

110) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $ 400 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Using the distribution above, what is the probability that during a randomly selected month PCE's were between $275.00 and $490.00?

A) .9579

B) .0421

C) .0001

D) .9999

111) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $400 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the point in the distribution below which 2.5% of the PCE's fell.

A) $ 390.00

B) $ 498.00

C) $ 10.00

D) $ 302.00

112) Before a new phone system was installed, the amount a company spent on personal calls followed a normal distribution with an average of $600 per month and a standard deviation of $50 per month. Refer to such expenses as PCE's (personal call expenses). Find the probability that a randomly selected month had PCE's below $450.

A) 0.0013

B) 0.2500

C) 0.9987

D) 0.7500

113) The preventable monthly loss at a company has a normal distribution with a mean of $8400 and a standard deviation of $40. A new policy was put into place, and the preventable loss the next month was $8160. What inference can you make about the new policy?

A) The new policy is probably less effective than the one it replaced.

B) Because the probability that the monthly loss would be as low as $8160 is not very small, the new policy is not working.

C) Because the probability that the monthly loss would be as low as $8160 is small, the new policy is working.

D) While the probability that the monthly loss would be as low as $8160 is small, it is not unexpected.

114) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 1200 miles. What is the probability a particular tire of this brand will last longer than 58,800 miles?

A) .1587

B) .2266

C) .7266

D) .8413

115) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2100 miles. What is the probability a certain tire of this brand will last between 55,590 miles and 56,220 miles?

A) .4649

B) .4920

C) .9813

D) .0180

116) The tread life of a particular brand of tire is a random variable best described by a normal distribution with a mean of 60,000 miles and a standard deviation of 2900 miles. What warranty should the company use if they want 96% of the tires to outlast the warranty?

A) 54,925 miles

B) 65,075 miles

C) 62,900 miles

D) 57,100 miles

117) The price of a gallon of milk follows a normal distribution with a mean of $3.20 and a standard deviation of $0.10. Find the price for which 12.3% of milk vendors exceeded.

A) $3.084

B) $3.238

C) $3.215

D) $3.316