Question: A selective college would like to have an entering class of 1200 students. Because not all students who are offered admission accept, the college admits more than 1200 students. Past experience shows that about 70% of the students admitted will accept. The college decides to admit 1500 students. Assuming that students make their decisions independently, the number who accept has the B(1500,0.7) distribution. If this number is less than 1200, the college will admit students from its waiting list.

a) What are the mean and the standard deviation of the number X of students who accept? (use the special formulas for the mean and standard deviation of a Binomial random variable)

b) Use the normal approximation to find the probability that at least 1000 student accept. (use the Normal approximation method; show your work)

c) The college does not want more than 1200 students. What is the probability that more than 1200 will accept?