document.write( "Question 1185987: A normal distribution has a standard deviation equal to 10. What is the mean of this normal distribution if the probability of scoring below x=10 is .5000? \n" ); document.write( "

Algebra.Com's Answer #816858 by Theo(13342) $\"\"$ $\"About$

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standard deviation is equal to 10.
\n" ); document.write( "probability of scoring below x = 10 is .5.\r
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\n" ); document.write( "\n" ); document.write( "the mean of a normal distribution has an area to the left of it and an area to the right of it equal to .5.\r
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\n" ); document.write( "\n" ); document.write( "that means the mean is right in the middle of the normal distribution.\r
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\n" ); document.write( "\n" ); document.write( "if the probability of scoring below x = 10 is .5, then x = 10 must be the mean of the normal distribution.\r
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\n" ); document.write( "\n" ); document.write( "if you want to go through the math, it will go like this.\r
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\n" ); document.write( "\n" ); document.write( "the z-score formula is:\r
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\n" ); document.write( "\n" ); document.write( "z = (x - m) / s\r
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\n" ); document.write( "\n" ); document.write( "the area to the left of a z-score of 0 is equal to .5.
\n" ); document.write( "x = 10
\n" ); document.write( "s = 10\r
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\n" ); document.write( "\n" ); document.write( "0 = (10 - m) / 10
\n" ); document.write( "multiply both sides of the equation by 10 to get:
\n" ); document.write( "10 * 0 = 10 - m
\n" ); document.write( "simplify to get:
\n" ); document.write( "0 = 10 - m
\n" ); document.write( "add m to both sides of the equation to get:
\n" ); document.write( "m = 10.\r
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