Question

I believe the answer to be 0.15 but I just want to make sureSuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.57 and a standard deviation of 0.44. Using the empirical rule, what percentage of the students have grade point averages that are greater than 3.89? Please do not round your answer

Answer 1

First, we need to find the z-score for the measure x=3.89. This is given by

`z=(x-\mu)/(\sigma)=(3.89-2.57)/(0.44)`

which gives

`z=3`

Now, from the empirical rule :

we can see that

`P(x>3.89)=P(z>3)\approx0.15\text{ \%}`

Then, the answer is 0.15%