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I had once learned the 16% from the gaussian distribution as a critical mass.
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2 standard deviations away from the median
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Just one actually, and from the mean of a normal distribution.
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One SD is 34 percent
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That's on both sides and it's 32. Two standard deviations is how the standard 95% confidence intervals are formed. That only leaves about 5%: https://www.z-table.com/
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1 standard deviation is 68 percent
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Yes and 100-68=32. The 16% refers to one of the tails of the distribution.
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I agree, where do you get that 16% number from?