document.write( "Question 1197916: Scores on a standardized exam are known to follow a normal distribution with standard deviation = 16. A researcher randomly selects 110 students and computes their average score. He reports that the mean score is 74.7, with a margin of error of 1.471.
\n" ); document.write( "How confident are you that the mean score for all students taking the exam is in the interval (73.229, 76.171)? \n" ); document.write( "
Algebra.Com's Answer #831395 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "E = margin of error
\n" ); document.write( "E = z*sigma/sqrt(n)
\n" ); document.write( "1.471 = z*16/sqrt(110)
\n" ); document.write( "1.471 = z*1.525540
\n" ); document.write( "z = 1.471/1.525540
\n" ); document.write( "z = 0.964249
\n" ); document.write( "z = 0.96\r
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\n" ); document.write( "\n" ); document.write( "Use a calculator like this
\n" ); document.write( "https://davidmlane.com/normal.html
\n" ); document.write( "to find that P(-0.96 < z < 0.96) = 0.6629 approximately
\n" ); document.write( "About 66.29% of the area under the curve is between z = -0.96 and z = 0.96\r
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\n" ); document.write( "\n" ); document.write( "The confidence level is about 66%
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