What are the answers for these problem? its one of the problems from normal dist

Question

What are the answers for these problem? its one of the problems from normal distribution. Please also give a explanation. Thanks

Every year, universities recruit students using their SAT scores. Based on the previous information, we know that SAT scores follows a normal curve with the mean 1000 and standard deviation 180. In the past, MSU admits students with SAT 1090 or higher. Q1: If MSU decides to raise the SAT admission limit to only admit the top 20% of high school graduates. What should be the new SAT admission limit? Q2: U of Michigan accept only the top 5% of their SAT scores. What is their minimum SAT score?

Explanation / Answer

Mean = 1000

Standard deviation = 180

P(X < A) = P (Z < (A - mean) / standard deviation)

If probability is known, the corresponding Z score shall be obtained from the standard normal distribution table and hence, from the Z score, the SAT score can be determined.

Q1. Let A be the admission limit of MSU

P(X > A) = 20% = 0.2

P(X < A) = 1 - 0.2 = 0.8

P(Z < (A -1000)/180) = 0.8

(A - 1000)/180 = 0.84

A = 1151.2

Q2. Let M be the minimum SAT score for acceptance in University of Michigan

P(X < M) = 1 - 0.05 = 0.95

P(Z < (M - 1000)/180 = 0.95

(M - 1000)/180 = 1.645

M = 1296.1

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