Question

Use the 68-95-99.7 rule to solve the problem.

At one college, GPA's are normally distributed with a mean of 3.4 and a standard deviation of 0.4. What percentage of students at the college has a GPA between 3.0 and 3.8?

Answer 1

68%

Explanation:

We are given the mean. We are told one deviation is .4. The 68 95 99.7 rule tells use that 68% is one deviation and 95 percent is two deviation and 99.7 is 3 deviations from the mean.

If the mean score is 3.4 and we add one deviation to that score we get

3.4 + .4 = 3.8

If we subtract one deviation, we get

3.4 - .4 = 3.0

This tells us that both GPA scores are one deviation from the mean. Knowing this, we can use our 68 95 99.7 rule that tells us that one deviation is 68% so the percentage of students at the college that has a GP between 3.0 and 3.8 is 68%