# Each of 100 multiple-choice questions on an exam has four possible answers, one of which is correct.

## Question:

Each of 100 multiple-choice questions on an exam has four possible answers, one of which is correct. For each question, a student guesses by selecting an answer randomly.

a. Specify the distribution of the student’s number of correct answers.

b. Find the mean and standard deviation of that distribution. Would it be surprising if the student made at least 50 correct responses? Why?

c. Specify the distribution of (n_{1}, n_{2}, n_{3}, n_{4}), where n_{j} is the number of times the student picked choice j.

d. Find E(n_{j}), var(n_{j}), cov(n_{j}, n_{k}), and corr(n_{j}, n_{k}).

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