document.write( "Question 1193873: Test scores are normally distributed with a mean of 76 and a standard deviation of 10.
\n" ); document.write( "a. In a group of 230 tests, how many students score above 96? \n" ); document.write( "
Algebra.Com's Answer #825920 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Calculate the z score
\n" ); document.write( "z = (x - mu)/sigma
\n" ); document.write( "z = (96 - 76)/10
\n" ); document.write( "z = (20)/10
\n" ); document.write( "z = 2
\n" ); document.write( "The raw score x = 96 is exactly two standard deviations above the mean.\r
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\n" ); document.write( "\n" ); document.write( "Then use a table like this
\n" ); document.write( "https://www.ztable.net/
\n" ); document.write( "to find that P(Z < 2) = 0.97725\r
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\n" ); document.write( "\n" ); document.write( "Which means,
\n" ); document.write( "P(Z > 2) = 1 - P(Z < 2)
\n" ); document.write( "P(Z > 2) = 1 - 0.97725
\n" ); document.write( "P(Z > 2) = 0.02275
\n" ); document.write( "and translates back to
\n" ); document.write( "P(X > 96) = 0.02275 when mu = 76 and sigma = 10\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Roughly 2.275% of the class scored above a 96
\n" ); document.write( "0.02275*230 = 5.2325 which rounds to 5\r
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\n" ); document.write( "\n" ); document.write( "Answer: 5 students
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