A test consists of 100 true–false questions. Joe did not study, so on each question he randomly guesses the correct response.

(a) Find the probability that he scores at least 70, thus passing the exam. (Hint: Use either the binomial distribution or the sampling distribution for the proportion of correct responses.)

(b) Jane studied a little and has a 0.60 chance of a correct response for each question. Find the probability that her score is nonetheless lower than Joe’s. (Hint: Usethe sampling distribution of the difference of sample proportions.)

(c) How do the answers to

(a) and

(b) depend on the number of questions? Explain.