Question 663874: For a certain mathematics class, the scores are normally distributed with a mean of 75 and a standard deviation of 8. The teacher wishes to give A’s to the top 6% of the students and F’s to the bottom 6%. The next 16% in either direction will be given B’s and D’s, with the other students receiving C’s. Find the bottom cutoff for the grades.
I have tried this problem about a dozen different ways, and I'm just confusing myself further. Any hints on how to get started the correct way? Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! it was a bit of a chore but i have the numbers you are looking for.
the problem comes in because the normal distribution curve doesn't stop at 100 but goes on indefinitely in both directions even though the percentages are very small.
i was, however, able to account for that by taking into account the area under the curve from 100 to infinity and then adding that to the 6% at the top end so that the percentages would work out.
to provide you with the details right now would take more time than i have so i'll just give you the answer and you can come back with further questions if you have them.
the numbers you are looking for are in the following table:
from to percentage under the normal distribution curve
0 62.56184 6%
62.56184 68.82248 16%
68.82248 81.152 55.91%
81.152 87.376 16%
87.376 100 6%
the total percent under the normal distribution curve comes out to be 99.91%
the remaining .09% is the area under the distribution curve that represents a score above 100.
that's where the difficulty was and what took the most time to figure out.
i started assuming 6% from the extreme right of the distribution curve but that gave me problem so i did a little digging and came up with the solution you see.
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