Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.
Estimate the percent within 1, 2, or 3 standard deviations of the mean using the empirical rule
Problem
Using the empirical rule, what percentage would you expect in this part of a normal model: within \(1~\text{sd}\) of mean?
Big Picture
What this problem is really about
Translate “within” into a central interval extending the same number of standard deviations on both sides of the mean. Then match that full band to the empirical rule: approximately 68, 95, and 99.7 percent fall within one, two, and three standard deviations in an approximately normal distribution. A mean-to-bound segment is only half of its symmetric central band.
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