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------------------------------------------------ A set of test scores is normally distributed with a mean of 100 and a standard deviation of 20. Use the 68−95−99.7 rule to find the percentage of scores greater than 100.

Using the 68-95-99.7 rule or the Empirical Rule, we find that approximately 84% of test scores are greater than 100 in a normal distribution with a mean of 100 and a standard deviation of 20.

Explanation:

The question pertains to a statistical rule called the 68-95-99.7 rule or the Empirical Rule. This rule is applicable to a normal distribution, which is a bell-shaped and symmetric statistical distribution. It states that in such a distribution, approximately 68 percent of the data is within one standard deviation of the mean, 95 percent is within two standard deviations, and 99.7 percent is within three standard deviations. Given this, if test scores have a normal distribution with a mean of 100 and a standard deviation of 20, the Empirical Rule can help us figure out the percentages of scores in certain categories. The category you're interested in are scores greater than 100. Since exactly half of the scores in a normal distribution are greater than the mean, this equates to 50 percent of scores. If we add half of the scores within one standard deviation of the mean (the 68% rule equates to 34% on either side of the mean), we find that approximately 84% of test scores are greater than 100.

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