Question

An exam is given to select the top 15% of incoming students for a special honors program. The cutscore for the exam is 28 points. The mean of the test scores is 24 points. What is the standard deviation of the test scores?

Answer 1

Solution:

Given: The cutscore for the top 15% students to the examination is 28 points.

Mean of test scores is 24.

That is

We have to find the standard deviation of test scores.

Assuming normal distribution and using z score formula we can find the value of standard deviation.

Since for top 15% have cut score =28

Then find corresponding z value.

That is find z such that

P(Z>z)=0.15

That is find z such that

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

P(Z<z)=1-0.15

P(Z<z)=0.85

Look in z table for area 0.8500 or its closest area and find corresponding z value.

From Z table we get area 0.8508 is closest to 0.8500 and it corresponds to z=1.0 and 0.04

Thus z= 1.04

Now use z score formula

Thus the standard deviation of test scores is