In each situation below, is it reasonable to use a binomial distribution for the random variable X? Give reasons for your answer in each case.
(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 (dimple, ripples, etc.) in the car's paint.
Each observation falls into a "success" or "failure."
There is a fixed number n of observations.
The n observations are all independent.
The probability of success p is the same for each observation.
None of the binomial conditions are met.
(b) The pool of potential jurors for a murder case contains 100 persons chosen at random from the adult residents of a large city. Each person in the pool is asked whether he or she opposes the death penalty. X is the number who say "Yes."
Each observation falls into a "success" or "failure."
There is a fixed number n of observations.
The n observations are all independent.
The probability of success p is the same for each observation.
None of the binomial conditions are met.
(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.
Each observation falls into a "success" or "failure."
There is a fixed number n of observations.
The n observations are all independent.
The probability of success p is the same for each observation.
None of the binomial conditions are met.