document.write( "Question 922356: You were told that the mean score on a business exam is 68 with the scores normally distributed. In addition, you know the probability of a score between 55 and 60 is 2.5% and that the probability of a score greater than 76 is 6.5%. What is the probability of a score between 55 and 76? \n" ); document.write( "
Algebra.Com's Answer #559491 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Something is wrong with this problem.  The two pieces of \r\n" );
document.write( "information given are inconsistent.  We only need that\r\n" );
document.write( "the mean is 68 and P(x > 76) = 0.065 to find the\r\n" );
document.write( "standard deviation, from which we can easily find  \r\n" );
document.write( "P(55 < x < 76).  \r\n" );
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document.write( "However using that standard deviation, We get that\r\n" );
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document.write( "P(55 < x < 60) = 0.058, not the 0.025 as is given.   \r\n" );
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document.write( "Here, I'll show this:\r\n" );
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\n" ); document.write( "the mean score on a business exam is 68
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document.write( "So \"mu=68\"\r\n" );
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\n" ); document.write( "the probability of a score greater than 76 is 6.5%
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document.write( "Therefore the z-score of x=76\r\n" );
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document.write( "We use a table or use a TI-83 or 84, to find the z-score\r\n" );
document.write( "such that the area to the right of it is 0.065.  We find \r\n" );
document.write( "that as z = 1.51.  That is,\r\n" );
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document.write( "P(z > 1.51) = 0.065\r\n" );
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document.write( "So want to substitute z = 1.51 x = 76 and \"mu=68\" in\r\n" );
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document.write( "\"z+=+%28x-mu%29%2Fsigma\" to find standard deviation \"sigma\"\r\n" );
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document.write( "But first we'll solve that for \"sigma\"\r\n" );
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document.write( "\"z%2Asigma+=+x-mu\"\r\n" );
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document.write( "\"sigma+=+%28x-mu%29%2Fz\"\r\n" );
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document.write( "Now we'll substitute:\r\n" );
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document.write( "\"sigma+=+%2876-68%29%2F1.51\"\r\n" );
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document.write( "\"sigma=5.284\"\r\n" );
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\n" ); document.write( "What is the probability of a score between 55 and 76?
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document.write( "That's easy, now that we have the standard deviation \"sigma=5.284\".\r\n" );
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document.write( "We find that to be 0.9281\r\n" );
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document.write( "We didn't even need this at all:\r\n" );
document.write( "

\n" ); document.write( "the probability of a score between 55 and 60 is 2.5%
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document.write( "However that is inconsistent with \"sigma=5.284\".\r\n" );
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document.write( "Because using the standard deviation that we calculated, that\r\n" );
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document.write( "P(55 < z < 60) = 0.058\r\n" );
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document.write( "So the two given pieces of information are inconsistent.\r\n" );
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document.write( "Edwin
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