A selective college would like to have an entering class of 900 students. Because not all students who are offered admission accept, the college admits more than 900 students. Past experience shows that about 78% of the students admitted will accept. The college decides to admit 1150 students. Assuming that students make their decisions independently, the number who accept has the B(1150, 0.78) distribution. If this number is less than 900, 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? 

b. The college does not want more than 900 students. Use the Normal approximation to find the probability that more than 900 students accept. 

c. If the college decides to decrease the number of admission offers to 1100, what is the probability that more than 900 will accept? 

d. Based on your answers to parts (b) and (c), should the college admit 1100 or 1150 students? Explain your answer