We wish to model a sampling situation from a population of 100 samples, where each will be evaluated as either a success or a failure.The proportion of "successes" in the population is known, and a sample without replacement is to be selected.It is proposed to use a binomial random variable to model probability in this model.Which of the following statements is accurate concerning this situation?
A) A binomial random variable would be accurate as long as the sampling process used is identical for each trial.
B) A geometric random variable would be better in this situation because the population is small and the sampling is without replacement.
C) A hypergeometric random variable would be better in this situation because the population is small and the sampling is without replacement.
D) A supergeometric random variable would be better in this situation because the population is small and the sampling is without replacement.

Question

Quizplus · Accepted Answer

A hypergeometric random variable is appropriate in this situation because it models the probability of selecting a specified number of successes in a sample of a certain size without replacement from a population of a certain size, which fits this situation. A binomial random variable assumes an independent sampling process with replacement, which is not the case in this situation. A geometric random variable models the probability of selecting the first success on a trial and is not appropriate in this situation. There is no such thing as a supergeometric random variable.

We Wish to Model a Sampling Situation from a Population