Question

A huge corporation which has recently had some bad publicity is trying to achieve a more positive public image. To do this, they are going to give out scholarships to high school students in STEM. To determine who gets the scholarships, the corporation gives a test to a large group of students. The scores are normally distributed with a mean score of 236 and standard deviation of 23. The big corporation does not want to give away too much money and decides they will only give scholarships to students with the top 5% of test scores. What is the lowest test score that they will offer a scholarship for?

Answer 1

Given that,

P(Z > 1.645) = 0.05

z = 1.645

Using z-score formula,

x = z * +

x = 1.645 * 23 + 236 = 273.835

Lowest test score = 273.835