What percent of observations are expected to fall between 2 and 3 standard deviations above (or below) the mean?

By the empirical rule, about 95% of observations are within 2 standard deviations of the mean, and about 99.7% are within 3. The difference, 99.7% − 95% = 4.7%, lies between 2 and 3 standard deviations on both sides combined. Half is on each side, so 4.7% ÷ 2 = 2.35% above or below the mean.

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