Here is a simple probability model for multiple-choice tests. Suppose that a student has probability p of correctly answering a question chosen at random from a universe of possible questions. (A good student has a higher p than a poor student.) The correctness of an answer to any specific question doesn't depend on other questions. A test contains n questions. Then the proportion of correct answers that a student gives is a sample proportion from an SRS of size n drawn from a population with population proportion p.

(a) Julie is a good student for whom p = 0.8. Find the probability that Julie scores 75% or lower on a 100 question test.

(b) If the test contains 250 questions, what is the probability that Julie will score 75% or lower? (Use the normal approximation to the sampling distribution to solve this problem.)