Use the Empirical Rule to Solve the Problem Note: the Sample Mean and Sample Standard Deviation of These

question 152

Multiple Choice

Use the empirical rule to solve the problem.
-Consider the following sample of exam scores, arranged in increasing order:
$\begin{array} { c c c c c c } 22 & 35 & 44 & 55 & 67 & 70 \\78 & 81 & 81 & 82 & 84 & 88 \\88 & 89 & 90 & 90 & 91 & 92 \\92 & 93 & 93 & 94 & 94 & 95 \\95 & 96 & 96 & 97 & 99 & 100\end{array}$
Note: The sample mean and sample standard deviation of these weights are, respectively, 82.4 and 19.5.

• A)(i)Use the Empirical rule to estimate the percentages of the observations that lie within 3 standard
• Deviation(s)to either side of the mean.
• (ii)Use the data to obtain the exact percentages of the observations that lie within 3 standard
• Deviation(s)to either side of the mean. (i)Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.4
• To 141.4;
• (ii)29 of the 30 observations (96.7%)lie between 23.4 and 141.4.
• B)(i)Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.9
• To 140.9;
• (ii)27 of the 30 observations 90% lie between 23.9 and 140.9.
• C)(i)Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 22.7
• To 142.7;
• (ii)30 of the 30 observations 100% lie between 22.7 to 142.7.
• D)(i)Assuming that the scores have a roughly bell-shaped distribution, approximately 99.7% of the observations should lie within 19.5 points of the mean 82.4 or within the interval from 23.9
• To 140.9;
• (ii)29 of the 30 observations (96.7%)lie between 23.9 and 140.9.

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