12.32 Multiple-choice tests. Here is a simple probability model for multiple-choice tests. Suppose that each student has probability p of correctly answering a question chosen at ran dom from a universe of possible questions. (A strong student has a higher p than a weak student.) Answers to different ques tions are independent.

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

(b) If the test contains 250 questions, what is the probability that Jodi will score between 70% and 80%? You see that Jodi's score on the longer test is more likely to he close to her "true score."