Question

Use the empirical rule to solve the problem.

At one college, GPA's are normally distributed with a mean of 2.9 and a standard deviation of 0.6. What percentage of students at the college have a GPA between 2.3 and 3.5? Please explain your answer, how you got the answer, formula. You can use excel to calculate but please show how to do it. Thanks

I found someone solved this below but I do not understand where 0.1587 came from.

P (2.3 < X < 3.5)
= 1 - P(X < 2.3) - P(X > 3.5)
= 1 - P(Z < ((2.3 - 2.9) / 0.6)) - P(Z > ((3.5 - 2.9) / 0.6))
= 1 - P(Z < -1) - P(Z > 1)
= 1 - 2P(Z > 1)
= 1 - 2(0.1587)
= 0.6826
This means 68.26% of the students have a GPA between 2.3 and 3.5
If you are using the empirical rule with 68% of the data lying within -1 < z < 1, then the answer will just be
68%

Answer 1

proportion of students at the college that have a GPA between 2.3 and 3.5 is

convert this to standard Z score

This means that these scores are within one standard deviation from the mean

Under the emperical rule, 68% of the data falls within one standard

now we know that normal distribution is symmetric which means that

(using excel formula =NORM.S.DIST(-1,TRUE))

Thus

=68.26%

I hope it helped. Please rate :)