23. A Skewed Distribution To study the usefulness of the Empirical Rule, look at a distribution that

Question:

23. A Skewed Distribution To study the usefulness of the Empirical Rule, look at a distribution that is heavily skewed to the right, as shown in the accompanying figure.

a. Calculate x and s for the data shown. (NOTE: There are 10 zeros, 5 ones, and so on.)

b. Find the intervals x 6s, x 62s, and x 63s and locate them on the graph.

c. Calculate the proportion of the n525 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 x 6s does not agree closely with the Empirical Rule, the proportions that fall into the intervals x 62s and x 63s agree very well. Many times this is true, even for non-mound-shaped distributions of data

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