document.write( "Question 577998: The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 10. What percent of the scores are greater than 87?? \n" ); document.write( "

Algebra.Com's Answer #370474 by Edwin McCravy(20055) $\"\"$ $\"About$

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The scores on an exam are normally distributed, with a mean of 77 and a standard deviation of 10. What percent of the scores are greater than 87??
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document.write( "Since 87 is 10, exactly 1 standard deviation, namely 10, above the mean, \r\n" );
document.write( "its z-score is 1.  Or we can calulate the z-score by formula:\r\n" );
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document.write( "Calculate the z-score\r\n" );
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document.write( "z =  =  =  = 1.\r\n" );
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document.write( "Anyway we want to find the percentage of area indicated by the\r\n" );
document.write( "shaded portion below to the right of z=1, which 1 standard deviation\r\n" );
document.write( "above the mean. \r\n" );
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document.write( "We are told that the middle region shaded below: \r\n" );
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document.write( "between z=-1 and z=+1 contains about 68.3% of the total\r\n" );
document.write( "area.  So the rest of the shaded area, which is this,\r\n" );
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document.write( "is 100% - 68.3% = 31.7% of the area, and therefore \r\n" );
document.write( "the desired percentage of area, which is this, \r\n" );
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document.write( "is half of 31.7%, and therefore about\r\n" );
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document.write( "15.9% \r\n" );
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document.write( "Edwin

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