document.write( "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.\r
\n" ); document.write( "\n" ); document.write( "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! \n" ); document.write( "

Algebra.Com's Answer #413103 by Theo(13342) $\"\"$ $\"About$

You can put this solution on YOUR website!
it was a bit of a chore but i have the numbers you are looking for.
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "the numbers you are looking for are in the following table:
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document.write( "from         to         percentage under the normal distribution curve\r\n" );
document.write( "0            62.56184               6%\r\n" );
document.write( "62.56184     68.82248               16%\r\n" );
document.write( "68.82248     81.152                 55.91%\r\n" );
document.write( "81.152       87.376                 16%\r\n" );
document.write( "87.376       100                    6%\r\n" );
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\n" ); document.write( "the total percent under the normal distribution curve comes out to be 99.91%
\n" ); document.write( "the remaining .09% is the area under the distribution curve that represents a score above 100.
\n" ); document.write( "that's where the difficulty was and what took the most time to figure out.
\n" ); document.write( "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.\r
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