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Suppose that each student has a 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. A student has p = .75.

a. Use the normal approximation to find the probability that the student scores 70% or lower on a 100-question test.
b. If the test contains 250 questions, what is the probability that the student scores 70% or lower?
c. How many questions must the test contain in order to reduce the standard deviation of the student's proportion of correct answers to half its value for a 100-item test.
d. A weaker student has p = .6. Does the answer you gave in (c) apply to this case also?

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