Question

GPAs are normally distributed with a mean of 2.6 and a standard deviation of 0.4. Using the Empirical Rule, what percentage of students at the college have a GPA between 2.2 and 3

Answer 1

2.2 = 2.6 - 0.4 is 1 standard deviation below the mean, and 3 = 2.6 + 0.4 is 1 standard deviation above it. Then by the empirical rule, the percentage of students with GPA between 2.2 and 3 is

Pr [2.2 ≤ X ≤ 3] = Pr [-1 ≤ Z ≤ 1] ≈ 68%

(where Z is normally distributed with mean 0 and s.d. 1)