You are taking a multiple choice exam consisting of eighty-eight questions, each of which has four possible responses exactly one of which is the correct response. suppose that you have not studied and so must randomly guess (select one of the four responses in such a way that each response is equally likely to be selected) on each question. Define X as the number of correct responses on the test.

a. note that X is a binomial random variable. state the four requirements necessary to establish this and explain why each of these requirements is valid in the context of this multiple choice exam.

b.What is your expected score on the test? Explain

C. Compute the standard deviation of X. Explain

D. What is the range of "ordinary" scores on the test? Explain how you define "ordinary"

E. Is it likely that you will answer at least forty-four questions correctly on the test? Explain.

F. John randomly guesses to answer each question. Is his score of thirty-four out of eighty-eight unusual? Explain