Use mean and standard deviation to fit normal distributions and estimate population percentages with technology.
Estimate a population percentage from a normal distribution using mean and standard deviation
Problem
What percentage of the population would you estimate in this normal distribution: mean \(100\) sd \(10\), between \(90\) and \(110\)?
Big Picture
What this problem is really about
Locate each bound relative to the mean by measuring its distance in standard deviations. If the bounds form a familiar symmetric band around the mean, apply the matching empirical-rule percentage; otherwise use standardized bounds or normal technology. Interpret the resulting area as an estimated proportion of the modeled population within the full interval, including both sides of the mean.
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