The director of a MPA program finds the incoming 200 students in the department with a mean GPA of 3.04 and a standard deviation of. 57. Assuming that students' GAPs are normally distributed, what is the range of GPA of 95% students

Question

Sienna Sweeney

Mathematics

21 October, 00:21

The director of a MPA program finds the incoming 200 students in the department with a mean GPA of 3.04 and a standard deviation of. 57. Assuming that students' GAPs are normally distributed, what is the range of GPA of 95% students

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Chan · Answer 1

The range of GPA of 95% students is from 1.9 to 3.18.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviation of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

Mean = 3.04

Standard deviation = 0.57

Assuming that students' GAPs are normally distributed, what is the range of GPA of 95% students

Within 2 standard deviations of the mean

3.04 - 2*0.57 = 1.9

3.04 + 2*0.57 = 3.18

The range of GPA of 95% students is from 1.9 to 3.18.