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.

1. Use the normal approximation to find the probability that Jodi scores 70% or lower on a 100-question test.
2. If the test contains 250 questions, what is the probability that Jodi will score 70% or lower?
3. 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?
4. 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?

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