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Question : Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount : 2163584

Provide an appropriate response.

41) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 14.14 onces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains more than 14.14 ounces of beer.

A) 0.4

B) 1

C) 0.5

D) 0

42) Suppose a brewery has a filling machine that fills 12 ounce bottles of beer. It is known that the amount of beer poured by this filling machine follows a normal distribution with a mean of 12.36 ounces and a standard deviation of 0.04 ounce. Find the probability that the bottle contains between 12.26 and 12.32 ounces.

A) 0.1525

B) 0.1649

C) 0.8475

D) 0.8351

43) The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 5.5 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will find a parking spot in the library parking lot in less than 5.0 minutes.

A) 0.2674

B) 0.3551

C) 0.3085

D) 0.1915

44) The length of time it takes college students to find a parking spot in the library parking lot follows a normal distribution with a mean of 6.0 minutes and a standard deviation of 1 minute. Find the probability that a randomly selected college student will take between 4.5 and 7.0 minutes to find a parking spot in the library lot.

A) 0.2255

B) 0.4938

C) 0.7745

D) 0.0919

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

45) A new car dealer observes that the number X of warranty claims for repairs on each new car sold is Poisson distributed, with an average of six claims per car. Compute the probability that a new car sold by the dealer will have no more than three warranty claims.

Enter your answer in the form ae^{b}.

46) In a certain office, the number of typewriters that break down during any given week is Poisson distributed with λ = 2. What is the probability that more than three typewriters break down during a week? Enter your answer in the form a ± (b/c)e^{d} where (b/c) is reduced.

47) Suppose the number of cars passing through a toll booth in a 10 minute interval is a Poisson random variable. If the average number of cars is 23, give an expression for the probability that n cars pass through the booth. Is p_{n} = ((23)^{n}/n!)e^{-23} correct?

Enter "yes" or "no".

48) Suppose a small amount of blood is sampled and the number of white blood cells are counted. If the number of white blood cells is Poisson distributed with λ = 6, what is the probability that the sample has more than 4 white blood cells? What is the average number of white blood cells per sample? Is Pr(4 ≤ X) = 0.7149; E(X) = 6 correct?

Enter "yes" or "no".

49) Suppose that during a certain part of the day, the number X of automobiles that arrive within any one minute at a tollgate is Poisson distributed, and Pr(X = k) = (4^{k} e^{-4}/1⋅2⋅...⋅k). What is the average number of automobiles that arrive per minute?

Enter just an integer.

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

50) Suppose X is a random variable whose probabilities are Poisson distributed with p_{n} = ((14)^{n}/n!)e^{-14}. Which of the following is true?

A) The standard deviation of X is 14.

B) The expected value of X is e^{-14}.

C) The probability that x = 0 is zero.

D) The probability that x = 14 is approximately 0.1060.

Use the Poisson Distribution to find the indicated probability.

51) If the random variable x has a Poisson Distribution with λ = 6, find p_{1}.

A) 0.04043

B) 0.00744

C) 0.01859

D) 0.01487

52) If the random variable x has a Poisson Distribution λ = 0.727, find p_{3}.

A) 0.00155

B) 0.03869

C) 0.03095

D) 0.13249

53) A naturalist leads whale watch trips every morning in March. The number of whales seen has a Poisson distribution with λ = 1.6. Find the probability that on a randomly selected trip, the number of whales seen is 3.

A) 0.1378

B) 0.2343

C) 0.2757

D) 0.4135

54) The number of lightning strikes in a year at the top of a particular mountain has a Poisson distribution with λ = 4.5. Find the probability that in a randomly selected year, the number of lightning strikes is 4.

A) 0.2467

B) 0.0063

C) 0.1898

D) 0.3227

55) The number of calls a mountain search and rescue team receives per day has a Poisson distribution with λ = 0.87. Find the probability that on a randomly selected day, they will receive fewer than two calls.

A) 0.2166

B) 0.1586

C) 0.3645

D) 0.7834

56) In one town, the number of burglaries in a week has a Poisson distribution with λ = 3.5. Find the probability that in a randomly selected week the number of burglaries is at least three.

A) 0.6792

B) 0.4634

C) 0.3208

D) 0.7842

E) 0.2158

SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

57) A person throws a die until the side with two spots appears. The probability of throwing the die exactly n times before throwing a "2" is ((5/6))^{n}((1/6)), n ≥ 0. What is the probability that the number of throws before throwing a "2" is even? Enter just a reduced fraction.

58) A basketball player attempts successive free throws until he succeeds in making a basket. Suppose the probability of success of each attempt is 0.7; thus, the probability of exactly n failures before the first success is (0.3)^{n}(0.7), n ≥ 0. What is the probability that the number of failures before the first successful free throw is odd? Enter just a reduced fraction.

59) Suppose that a bag holds 3 blue balls and one red ball. We pull a ball from the bag at random, return it and then repeat the process. Suppose we continue pulling balls until the blue ball is drawn and then we observe the number of consecutive red balls drawn. What is the average number of red balls between occurrences of blue balls? Is

correct? Enter "yes" or "no".