Question

Determine whether the given procedure results in a binomial distribution​ (or a distribution that can be treated as​ binomial). If the procedure is not​ binomial, identify at least one requirement that is not satisfied. Five different senators from the current U.S. Congress are randomly selected without replacement and whether or not​ they've served over 2 terms is recorded. Does the probability experiment represent a binomial​ experiment? A. ​No, because the experiment is not performed a fixed number of times. B. ​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial. C. ​Yes, because the experiment satisfies all the criteria for a binomial experiment. D. ​No, because there are more than two mutually exclusive outcomes for each trial.

Answer 1

B. ​No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.

Explanation:

The first criterion of a binomial distribution is a fixed number of trials. Selecting 5 senators means the number of trials is 5, which is a fixed number.

The next criterion is that the trials must be independent. Selecting the senators without replacement means the trials are dependent, not independent; this means that this is not a binomial distribution.