What is the minimum score required for admission?

Question

Suppose ACT Mathematics scores are normally distributed with a mean of 20.8 and a standard deviation of 5.4. A university plans to admit students whose scores are in the top 30%

Answer 1

Obtain a z-score chart:

http://www.utdallas.edu/dept/abp/zscoretable.pdf

 

The top 30% are those who have 70% below.

The z-score for 70% is approximately 0.525

 

0.525 = (X - 20.8) / 5.4

2.835 = X - 20.8

23.635 = X