14.35 Multiple-choice tests. Here is a simple probability model for multiple-choice tests. Suppose 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.) Answers to different questions are independent.

(a) Stacey is a good student for whom p ! 0.75. Use the Normal approximation to find the probability that Stacey scores between 70% and 80% on a 100-question test.

(b) If the test contains 250 questions, what is the probability that Stacey will score between 70% and 0%? You see that Stacey’s score on the longer test is more likely to be close to her “true score.”