How to find the probability for Normal approximation of Binomial distribution
Confessing students to college. A discriminating college would like to have an entering class of 950 students. Because not entirely students who are offered admission accept, the college admits more than 950 students. Past experience appearances that about 75% of the students admitted will accept. The college elects to admit 1200 students. Presumptuous that students make their decisions independently, the number who accept has the B (1200, 0.75) distribution. If this number is less than 950 the college will admit students from its waiting list.
a) Explain what are the mean and standard deviation of the number X of students who accept?
b) Explain the college does not want more than 950 students. Explain what is the probability that more than 950 will accept?
c) Explain if the college decides to increase the number of admission offers to 1300 and what is the probability that more than 950 will accept?