Question

determine whether the following procedure results in a binomial distribution or a distribution that can be treated as binomial (by applying the 5% guideline for cumbersome calculations). if it is not binomial and cannot be treated as binomial, identify at least one requirement that is not satisfied.
the senate members of the 116th congress include 75 males and 25 females. forty different senators are randomly selected without replacement, and the gender of each selected senator is recorded.
choose the correct answer below.
a. it is binomial or can be treated as binomial.
b. it is not binomial because there are more than two mutually exclusive outcomes for each trial.
c. it is not binomial because the selections are not independent. (the 5% guideline for cumbersome calculations should not be used.)
d. it is not binomial because the experiment is not performed a fixed number of times.

Explanation:

A binomial distribution requires a fixed number of independent trials, each with two mutually - exclusive outcomes (success or failure), and a constant probability of success. Here, the selections are not independent (sampling without replacement). The 5% guideline (if \(n\leq5\%\) of \(N\), we can treat sampling without replacement as independent) is not met since \(n = 40\) and \(N=100\) (\(40>5\%\) of \(100 = 5\)).

Answer:

C. It is not binomial because the selections are not independent. (The 5% guideline for cumbersome calculations should not be used.)