Question

determine if the following probability experiment represents a binomial experiment. if not, explain why. if the probability experiment is a binomial experiment, state the number of trials, n. an experimental drug is administered to 30 randomly selected individuals, with the number of individuals responding favorably recorded. select the correct choice below and, if necessary, fill in the answer box to complete your answer. o a. yes, because the experiment satisfies all the criteria for a binomial experiment, n = (type a whole number) o b. no, because the trials of the experiment are not independent because the probability of success differs from trial to trial. o c. no, because there are more than two mutually exclusive outcomes for each trial. o d. no, because the experiment is not performed a fixed number of times.

Explanation:

Step1: Check binomial experiment criteria

A binomial experiment has the following criteria:

• A fixed number of trials \(n\).
• Each trial has only two mutually - exclusive outcomes (success or failure).
• The probability of success \(p\) is the same for each trial.
• The trials are independent.

In this experiment, the drug is administered to 30 randomly selected individuals (\(n = 30\) fixed number of trials). Each individual either responds favorably (success) or not (failure) (two mutually - exclusive outcomes). Since the individuals are randomly selected, we can assume the probability of a favorable response is the same for each individual and the responses of one individual do not affect the responses of others (independent trials).

Answer:

A. Yes, because the experiment satisfies all the criteria for a binomial experiment, \(n = 30\)