finding percentile from z-score


New Member
I have this question which i am so confused how to solve it

this is on normal curve. The following table is used to determine the student’s grades:

Grade       Z-score 
A above    1.5 
B              0.5-1.5 
C             -0.5 to 0.5 
D             -1.5 to -0.5 
F              Below-1.5
Using this system, what percent of As Bs, Cs Ds and Fs are expected with a normal distribution of scores?

Now, I know the distribution is distributed in -2.1% - 13.4% - 34.1% (on both sides). It would have been easier if i could imagine that mean is 0 and sd is 1. but the above distribution doesn't match if i assume SD is 1 since the gap between 0.5 is 1 and then its 1 and so on (not sure if i am making any sense, I am just trying to think).

I am unable to put a finger how to go about this problem.

Seems to me that the area of the curve above/between/below these z values is the corresponding percent of students expected to get the grade. For example, P(Z>1.5)=.0668 This means that 6.68% of students are expected to get an A. Hint: After you are finished with the problem, these percents should add to 1.