Question

A college administrator states that the average high school GPA for incoming freshman is normally distributed with a mean equal to 3.30 and a standard deviation equal to .20. If students with a GPA in the top 10% will be offered a scholarship, then what is the minimum GPA required to receive the scholarship?

Answer 1

Explanation:

First, we get the z score from the given left tailed area. As

Left tailed area = 1 - 0.10 = 0.9

Then, using table or technology,

z = 1.281551566

As x = u + z * s,

where

u = mean = 3.3

z = the critical z score = 1.281551566

s = standard deviation = 0.2

Then

x = critical value = 3.556310313