Normal Distribution and Grade Cut-offs

Hello, I tried googling this question, watching how-to videos, and read over the chapter in my textbook several times but I cannot seem to understand how to go about solving this question.

The following question applies to a normal distribution of statistics test scores with a mean of 100 and a standard deviation of 40.

The teacher decided to give the top 30% of the class a grade of A, the next 40% of students a grade of B, and the final 30% a grade of C. What are the test scores that correspond to these grade cut-offs?

Example questions I found on google always specified how many students actually took the test. But since it does not specify that in this question, how would I go about solving this?

Any help would be greatly appreciated.
I found one example problem but do not understand what they mean by this step:

Step 2: Selecting the top 15% involves finding out that value of z = k pertaining to the cut - off score. From the diagram, P(0 < z < k) = 0.50 - 0.15 = 0.35.


Less is more. Stay pure. Stay poor.
Do you get to use the standard normal table?

Quite a few assumptions have to be made, but since this is a problem we will assume they are met. So when you go to the standard normal table and look-up 0.90 you get a value of 1.29. What is that number and can it be used?
Yes we get to use the standard normal table. Isn't .90 the top 10 %? Would I need to look up the top 30%?

Also I figured out how to do this problem on a calculator, Distribution -> invNorm (.70) -> .5244 (x40 + 100) = 120.97 (which is the cut off for top 30% I believe?)

I do not understand how to solve this problem without using the calculator though, could anyone provide some insight?
I also think approximately 121 is the correct answer. If you just NORMALCDF(0, 121, 100, 40) on your calculator, you get about .70, which would then imply that 121 and up is the top 30%.


Less is more. Stay pure. Stay poor.
The second or third page of the link I posted tells you how to calculate it by had using the exact same 90% cut-off. It doen't get any clearer than that!