Answer :
Final answer:
The 68-95-99.7 rule states that for a bell-shaped and symmetric distribution, a certain percentage of data falls within a certain number of standard deviations from the mean. To find the percent of values below a standard deviation, you need to determine the corresponding percentile. For example, one standard deviation corresponds to the 68th percentile.
Explanation:
The 68-95-99.7 rule, also known as the Empirical Rule, states that for data with a bell-shaped and symmetric distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and more than 99% falls within three standard deviations.
To find the percent of values below a certain standard deviation using this rule, you need to determine the corresponding percentile. For example, if you want to find the percent of values below one standard deviation, you would look for the 68th percentile. If you want to find the percent below two standard deviations, you would look for the 95th percentile. You can use a calculator or a normal distribution table to find the corresponding percentiles. Let's say you want to find the percent of values below one standard deviation. The corresponding percentile is the difference between 50% and (50% - 68%), which is 84%. This means that 84% of the values will be below one standard deviation.
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