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.
B. No, because the trials of the experiment are not independent and the probability of success differs from trial to trial.
Step-by-step 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.
