# Thread: Help with normal distribution/mean question

1. ## Help with normal distribution/mean question

I'm having trouble with this seemingly easy question:

On an exam with normally distributed grades, 32 points put you at the border of the bottom 2.5% of your class, while 97 points puts you right at the top 0.15%.
a. What is the class average grade?
b. What is the z-score for a grade of 65?
c. What percentile is a grade of 58?

For part a, I know that the bottom 2.5% is 2 standard deviations away from the mean, but I don't understand how you can find the mean with just that information. There's also the 97 points is the top .15%, but .15% isn't a clear-cut SD number like 2.5% is. So 32 points is 2 standard deviations away from the mean, and 97 is the top .15%...I'm not sure where to go from here.

b and c, I can't do those without the class mean, right?

2. Originally Posted by pianopiano
I'm having trouble with this seemingly easy question:

On an exam with normally distributed grades, 32 points put you at the border of the bottom 2.5% of your class, while 97 points puts you right at the top 0.15%.
a. What is the class average grade?
b. What is the z-score for a grade of 65?
c. What percentile is a grade of 58?

For part a, I know that the bottom 2.5% is 2 standard deviations away from the mean, but I don't understand how you can find the mean with just that information. There's also the 97 points is the top .15%, but .15% isn't a clear-cut SD number like 2.5% is. So 32 points is 2 standard deviations away from the mean, and 97 is the top .15%...I'm not sure where to go from here.

b and c, I can't do those without the class mean, right?

$\mu + 3 \sigma = 97$ .... (1)
$\mu - 2 \sigma = 32$ .... (2)
Solve equations (1) and (2) simultaneously for $\mu$ and $\sigma$.