A selective college would like to have an entering class of 950 students. Becaus

Question

A selective college would like to have an entering class of 950 students. Because not all students who are offered
admission accept, they admit more than 950 students, knowing that only about 75% of the students admitted will accept.
The college decides to admit 1200 students. Then N = 1200 and P = 0.75 (assuming students make their decisions
independently). If the number who accept is less than 950, they will admit students from a waiting list.

a) Use the Normal approximation to find P(X is at least 800).

b) Use the Normal approximation to find P(X > 950).
c) If the college decides to increase the number of admission offers to 1300, estimate P(X > 950).

Explanation / Answer

= np = 1200 * 0.75 = 900, = (npq) = (1200 * 0.75 * 0.25) = 15

(a) z = (x - )/ = (799.5 - 900)/15 = -6.7

P(x 800) = P(z > -6.7) = 1

(b) z = (950.5 - 900)/15 = 3.3667

P(x > 950) = P(z > 3.3667) = 0.0004

(c) = np = 1300 * 0.75 = 975 and = (npq) = sr91300 * 0.75 * 0.25) = 15.61

z = (950.5 - 975)/15.61 = -1.5695

P(x > 950) = P(z > -1.5695) = 0.9417

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