document.write( "Question 615720: Please show all of your work when answering the following:
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\n" ); document.write( "I. Use Chebyshev’s theorem to find what percent of the values will fall between 237 and 297 for a data set with a mean of 267 and standard deviation of 15.
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\n" ); document.write( "II. Use the Empirical Rule to find what two values 95% of the data will fall between for a data set with a mean of 207 and standard deviation of 20.
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mean is 267
\n" ); document.write( "standard deviation is 15
\n" ); document.write( "score of 237 = z-score of (237-267)/15 = -2.0
\n" ); document.write( "score of 297 = z-score of (297-267)/15 = +2.0
\n" ); document.write( "k value = 2 standard deviations.
\n" ); document.write( "chebyshev states that the probability of scores being within this range will be greater than or equal to p = 1 - (1/k^2)
\n" ); document.write( "since k is equal to 2, this means that:
\n" ); document.write( "p = 1 - (1/4) which means that p = 3/4 which means that p = .75 or 75%.
\n" ); document.write( "this means that the probability that the scores will be between 237 and 297 is greater than or equal to 75%.
\n" ); document.write( "here's a reference that details how this calculation is made:
\n" ); document.write( "http://answers.yahoo.com/question/index?qid=20070914074905AAasH9q
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