You are to take a multiple-choice exam consisting of 100 questions with five possible responses to each. 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 r.v. X represent the number of correct responses on the exam.2
(a) Specify the probability distribution of X.
(b) What is your expected number of correct responses?
(c) What are the values of the variance and standard deviation of X?
(d) Based on your answers to parts (b) and (c), is it likely that your number of correct responses would be more than 50? Explain the reasoning behind your answer using Tchebysheff's Theorem.
(e) What is the approximate probability that your number of correct responses will be between 15 and 30 (inclusive)? More than 25?Less than 35?