Here is a simple probability model for multiple-choice tests.Suppose that each student has probability p of correctly answeringa question chosen at random from a universe of possible questions.(A strong student has a higher p than a weak student.) Thecorrectness of answers to different questions are independent. Jodiis a good student for whom p = 0.8.
(a) Use the Normal approximation to find the probability thatJodi scores 74% or lower on a 100-question test. (Round your answerto four decimal places.)
(b) If the test contains 250 questions, what is the probabilitythat Jodi will score 74% or lower? (Use the normal approximation.Round your answer to four decimal places.)
(c) How many questions must the test contain in order to reducethe standard deviation of Jodi's proportion of correct answers tohalf its value for a 100-item test?
