Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A strong student has a higher p than a weak student.) The correctness of answers to different questions are independent. Jodi is a good student for whom p = 0.85.
(a). Use the normal approximation to find the probability that Jodi scores 78% or lower on a 100-question test.
(b). If the test contains 250 questions, what is the probability that Jodi will score 78% or lower?
(c). How many questions must the test contain in order to reduce the standard deviation of Jodi's proportion of correct answers to half its value for a 100-item test?