In each situation, is it reasonable to use a binomial distribution for the random variable X? If the situation is not reasonable for a binomial distribution, select the correct statement that explains why.
(a) An auto manufacturer chooses one car from each hour's production for a detailed quality inspection. One variable recorded is the count X of finish defects (dimples, ripples, etc.) in the car's paint. Is it reasonable to use a binomial distribution for the random variable X? Select an answer choice.
A binomial distribution is not reasonable because there are more than two outcomes of interest.
A binomial distribution is not reasonable because ?p is not constant.
A binomial distribution is not reasonable because ?n is not fixed.
Yes, a binomial distribution is reasonable.
A binomial distribution is not reasonable because trials are not independent.
(b) The pool of potential jurors for a murder case contains 100 people chosen at random from the adult residents of a large city. Each person in the pool is asked in private whether he or she opposes the death penalty; X is the number who say "Yes." Is it reasonable to use a binomial distribution for the random variable X? Select an answer choice.
A binomial distribution is not reasonable because ?p is not constant.
A binomial distribution is not reasonable because there are more than two outcomes of interest.
A binomial distribution is not reasonable because trials are not independent.
A binomial distribution is not reasonable because ?n is not fixed.
Yes, a binomial distribution is reasonable.
(c) Joe buys a ticket in his state's Pick 3 lottery game every week; X is the number of times in a year that he wins a prize. Is it reasonable to use a binomial distribution for the random variable ?? Select an answer choice.
Yes, a binomial distribution is reasonable.
A binomial distribution is not reasonable because trials are not independent.
A binomial distribution is not reasonable because n is not fixed.
A binomial distribution is not reasonable because p is not constant.
A binomial distribution is not reasonable because there are more than two outcomes of interest.
Ans:
(a)A binomial distribution is not reasonable because n is not fixed.
(b) Yes, a binomial distribution is reasonable.
A binomial distribution is reasonable here; a “large city” will have a population much larger than 100 (the sample size), and each randomly selected juror has the same (unknown) probability p of opposing the death penalty.
n=100 and p=0.5
(c)Yes, a binomial distribution is reasonable.
In a Pick 3 game, Joe’s chance of winning the lottery is the same every week, so assuming that a year consists of 52 weeks (n=52 ), this will have binomial distribution.
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