Question

On a certain standardized test used for college entrance purposes, the mean score was 21 and the standard deviation was 5. The distribution was approximately normal. Carlos scored 31, two standard deviations above the mean. A total of 1.5 million people across the country took the test at the same time as Carlos. How many people had scores lower than Carlos?

a. 1,465,500 people
b. 977,000 people
c. 204,000 people

Answer 1

A

Explanation:

Carlos' score was 2 standard deviations from the mean, so his z-score was 2.0. You can either use the empirical 68-95-98.5 rule, or you can plug it into your calculator as normalcdf(-999, 2) = .977

So 97.7% of people had a score lower than Carlos!

.977 * 1.5 million = 1,465,500 people