Question 4: Solve this problem. Admitting students to college. 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 the B(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 number X of students who ассept? (b) Use the Normal approximation to find the probability that at least 800 students ассept. (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?

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Question 4: Solve this problem.
Admitting students to college. 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 de
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.
les to adr
1200 students. Assuming that students
(a) What are the mean and the standard deviation of the number X of students who
ассept?
(b) Use the Normal approximation to find the probability that at least 800 students
ассept.
(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?
Transcribed Image Text:3 Question 4: Solve this problem. Admitting students to college. 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 de 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. les to adr 1200 students. Assuming that students (a) What are the mean and the standard deviation of the number X of students who ассept? (b) Use the Normal approximation to find the probability that at least 800 students ассept. (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?
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