document.write( "Question 617669: a set of data is normally distributed with a mean of 1000 and a standard deviation of 100 what would be standard score for a score of 900 what percent of scores is between 1000 and 900 what would be percentile rank for a score of 900 \n" ); document.write( "

Algebra.Com's Answer #388547 by Theo(13342) $\"\"$ $\"About$

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mean = 1000
\n" ); document.write( "standard deviation = 100
\n" ); document.write( "standard score = z-score
\n" ); document.write( "standard score for 900 would be equal to:
\n" ); document.write( "(900 - 1000) / 100 = -1.0
\n" ); document.write( "A score of 900 is 1 standard deviation below the mean which would have a standard score of 0.
\n" ); document.write( "the area to the left of a z-score of -1 is equal to .1587
\n" ); document.write( "the area to the left of a z-score of -0 is equal to .5
\n" ); document.write( "the area between a z-score of 0 and a z-score of -1 is therefore equal to .5 - .1587 which is equal to .3413.
\n" ); document.write( "since a z-score of -1 is equivalent to a score of 900 and a z-score of 0 is equivalent to a score of 1000 for this problem, this means that 34.13% of the area under the normal distribution curve is between 900 and 1000.
\n" ); document.write( "The percentile rank of a score of 900 would be equal to 15.87% because a score of 900 is better than 15.87% of all the scores.
\n" ); document.write( "here's a reference on percentile rank.
\n" ); document.write( "http://davidmlane.com/hyperstat/A79567.html
\n" ); document.write( "here's a reference on z-scores.
\n" ); document.write( "http://www.measuringusability.com/zcalc.htm
\n" ); document.write( "here's a reference on normal distribution curves
\n" ); document.write( "http://www.regentsprep.org/Regents/math/algtrig/ATS2/NormalLesson.htm
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