Question

Determine whether the experiment is a binomial experiment. If it is, specify the values of n,p, and q, and list the possible values of the random variable x. If it is not, explain why.

You take a multiple-choice quiz that consists of 10 questions. Each question has four possible answers, only one of which is correct. To complete the quiz, you randomly guess the answer to each question. The random variable represents the number of correct answers.
a. Identify a trial of the experiment and what is a success.
b. Determine whether the experiment satisfies the four conditions of a binomial experiment.
c. Make a conclusion and identify n,p,q, and the possible values of x, if possible.

Answer 1

In this multiple-choice quiz experiment, the number of trials is 10, the success is answering a question correctly, and the probability of success (p) is 1/4 while the probability of failure (q) is 3/4.

Step-by-step explanation:

A binomial experiment has three characteristics: a fixed number of trials, two possible outcomes (success and failure), and independent trials with the same probability of success. In this multiple-choice quiz experiment, the number of trials is 10, the success is answering a question correctly, and the probability of success (p) is 1/4 while the probability of failure (q) is 3/4. The random variable (X) represents the number of correct answers, and the possible values of X range from 0 to 10.