10.122 Guessing on a test A test consists of 100 true-false questions.

Joe did not study, and on each question he randomly guesses the correct response. Jane studied a little and has a 0.60 chance of a correct response for each question.

a. Approximate the probability that Jane’s score is nonetheless lower that Joe’s. (Hint: Use the sampling distribution of the difference of sample proportions.)

b. Intuitively, do you think that the probability answer to part a would decrease or increase if the test had only 50 questions? Explain.