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 answers to different questions are independent. jodi is a good student for whom p = 0.76. use 4 decimal places.

(a) if the test contains 250 questions, what is the probability that jodi will score 71% or lower?
(b) how many questions must the test contain in order to reduce the standard deviation of jodi's proportion of correct answers to half its value for a 100-item test?