7.55 You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question.

Let x represent the number of correct responses on the test.

a. What kind of probability distribution does x have?

b. What is your expected score on the exam? (Hint:

Your expected score is the mean value of the x distribution.)

c. Compute the variance and standard deviation of x.

d. Based on your answers to Parts

(b) and (c), is it likely that you would score over 50 on this exam?
Explain the reasoning behind your answer.