Question

Suppose the gpa scores of the students in a class are normally distributed with a mean of 3.4 and a standard deviation of 0.2 . Use the empirical rule to find the percentage of students in this class with a GPA
Between 3.2 and 3.6 ( 1 standard deviation)

Answer 1

Suppose the gpa scores of the students in a class are normally distributed with a mean of 3.4 and a standard deviation of 0.2

We need to find how far 3.2 from 3.4

3.4 - 3.2 = 0.2  that is 1 standard deviation from mean (left)

Also we find how far 3.6 from 3.4

3.6 - 3.4 = 0.2  that is 1 standard deviation from mean (right)

As per empirical rule , 68% of values fall within 1 standard deviation from mean

so 68% of students in this class with a GPA  Between 3.2 and 3.6