document.write( "Question 1181628: A distribution of values is normal with a mean of 199.9 and a standard deviation of 82.\r
\n" ); document.write( "\n" ); document.write( "Find P57, which is the score separating the bottom 57% from the top 43%. \r
\n" ); document.write( "\n" ); document.write( "P57 = \r
\n" ); document.write( "\n" ); document.write( "Enter your answer as a number accurate to 4 decimal places. \n" ); document.write( "
Algebra.Com's Answer #811786 by Theo(13342)\"\" \"About 
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mean = 199.9
\n" ); document.write( "standard deviation = 82
\n" ); document.write( "p57 = area to the left of the z-score.
\n" ); document.write( "z-score with area to the left of it equal to .57 = .1763741565 = (
\n" ); document.write( "use the z-score formula to find the raw swcore.
\n" ); document.write( "z = (x - m) / sd
\n" ); document.write( "z is the z-score
\n" ); document.write( "x is the raw score
\n" ); document.write( "m is the mean
\n" ); document.write( "sd is the standard deviation
\n" ); document.write( "formula becomes:
\n" ); document.write( ".1763741565 = (x - 199.9) / 82
\n" ); document.write( "solve for x to get:
\n" ); document.write( "x = 82 * .1763741565 + 199.9 = = 214.3626808
\n" ); document.write( "round your answer to 4 decimal places to get:
\n" ); document.write( "x = 214.3627
\n" ); document.write( "this is the raw score that has 57% of the area under the normal distribution curve to the left of it and 43% of the area under the normal distribution curve to the right of it.\r
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\n" ); document.write( "\n" ); document.write( "on a graph, it looks like this:\r
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