Question

Suppose SAT Writing scores are normally distributed with a mean of 497 and a standard deviation of 109. A university plans to award scholarships to students whose scores are in the top 8%. What is the minimum score required for the scholarship? Round your answer to the nearest whole number, if necessary.

Answer 1

Solution:

Given: SAT Writing scores are normally distributed with a mean of 497 and a standard deviation of 109.

A university plans to award scholarships to students whose scores are in the top 8%.

We have to find the minimum score required for the scholarship.

That is find x value such that:

P(X > x ) =8%

P(X > x ) =0.08

Thus find z value such that:

P( Z > z ) =0.08

That is find z such that:

P( Z < z ) = 1 - P( Z> z )

P( Z < z ) = 1 - 0.08

P( Z < z ) = 0.92

Look in z table for Area = 0.9200 or its closest area and find corresponding z value.

Area 0.9207 is closest to 0.9200 and it corresponds to 1.4 and 0.01

Thus z = 1.41

Now use following formula to find x value: