Question 4: Solve this problem.

A selective college would like to have an entering class of 950 students. Because not all students who are offered admission accept, the college admits more than 950 students. Past experience shows that about 75% of the students admitted will accept. The college decides to admit 1200 students. Assuming that students make their decisions independently, the number who accept has theB(1200, 0.75) distribution. If this number is less than 950, the college will admit students from its waiting list.

(a) What are the mean and the standard deviation of the numberXof students who accept?

(b) Use the Normal approximation to find the probability that at least 800 students accept.

(c) The college does not want more than 950 students. What is the probability that more than 950 will accept?

(d) If the college decides to increase the number of admission offers to 1300, what is the probability that more than 950 will accept?