Question: 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 an answer to a question is independent of the correctness of answers to other questions. Jodi is a good student for whom p=0.75.

a. Use the normal approximation to find the probability that Jodi scores 70% or lower on a 100-question test.

b. If the test contains 250 questions, what is the probability that Jodi will score 70% or lower?

c. How many questions must the test contain in order to reduce the standard deviating of Jodi’s proportion of correct answers to half its value for a 100 item test?

d. Laura is a weaker student for whom p=0.6. Does the answer you gave in © for the standard deviation of Jodi’s score apply to Laura’s standard deviation also?