At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. Using the empirical rule, what percentage of students at the college have a GPA between 2.3 and 3.5? 84.13% 68% 99.7% 95%

68% of the data values lie within one standard deviation from the mean i.e. from z = -1 to z = 1 we have 68% of the data values
95% of the data values lie within two standard deviations of the mean
99.7% of the data values lie within three standard deviations of the mean

So first we have to find how many standard deviations away from the mean are the given two values. This can be done by converting them into z scores.

The formula to calculate the z-score is:

[tex]z=\frac{\text{Data Value}-\text{Mean}}{\text{Standard Deviation}}[/tex]

Using the given values in above formula, we get:

For x = 2.3

[tex]z = \frac{2.3-2.9}{0.6}=-1[/tex]

For x = 3.5

[tex]z = \frac{3.5-2.9}{0.6}=1[/tex]

This means we have to tell how many data values are within one standard deviation of the mean. According to the empirical rule 68% of the values are between z= -1 and z = 1. So the answer is 68%

raphealnwobi raphealnwobi · Answer 2 · 2022-04-07T11:36:17+02:00

68% of students at the college have a GPA between 2.3 and 3.5.

What is the empirical rule?

The empirical rule states that for a normal distribution, 68% of the values falls within one standard deviation, 95% of the values falls within two standard deviation, and 99.7% of the values falls within three standard deviation.

Hence:

For a mean of 2.9 and a standard deviation of 0.6.

68% falls within 2.9 ± 0.6 = (2.3, 3.5)

68% of students at the college have a GPA between 2.3 and 3.5.

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