Question

A mandatory competency test for high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100. if the top 3% of students receive $500, find the minimum score you would need to receive this award.

Answer 1

To solve for the minimum score required, we find for the z score value at P = 0.97 (top 3%). The z score is:

z = 1.88

Then we use the formula to find for X:

z = (X – u) / s

1.88 = (X – 400) / 100

X = 588

 

You have to score at least 588.