(Solution) - To illustrate the utility of the Empirical Rule consider a -(2025 Original AI-Free Solution)

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To illustrate the utility of the Empirical Rule, consider a distribution that is heavily skewed to the right, as shown in the accompanying figure.
a. Calculate  and s for the data shown.
b. Construct the intervals ± s, ± 2s, and ± 3s and locate them on the frequency distribution.
c. Calculate the proportion of the n = 25 measurements that fall into each of the three intervals. Compare with Tchebysheff's Theorem and the Empirical Rule. Note that, although the proportion that falls into the interval ± s does not agree closely with the Empirical Rule, the proportions that fall into the intervals ± 2s and ± 3s agree very well. Many times this is true, even for non-mound-shaped distributions of data.