This is not a symmetrical interval – this is merely the probability that an observation is less than μ + 2 σ . To compute the probability that an observation is within two standard deviations of the mean (small differences due to rounding): Main article: Normality test. One can compute more precisely, approximating the number of extreme moves of a given magnitude or greater by a Poisson distribution, but simply, if one has multiple 4 standard deviation moves in a sample of size 1,000, one has strong reason to consider these outliers or question the assumed normality of the distribution. Because of the exponentially decreasing tails of the normal distribution, odds of higher deviations decrease very quickly. From the rules for normally distributed data for a daily event: See also Edit. ”The Normal Distribution” by Balasubramanian Narasimhan ”Calculate percentage proportion within x sigmas at WolframAlpha.
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