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A Logical Introduction to Probability and Induction. In mathematical notation, these facts can be expressed as follows, where Pr() is the probability function, Χ is an observation from a normally distributed random variable, μ (mu) is the mean of the distribution, and σ (sigma) is its standard deviation: In statistics, the 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie withinĪn interval estimate in a normal distribution: 68%, 95%, and 99.7% of the values lie within one, two, and three standard deviations of the mean, respectively. The y-axis is logarithmically scaled (but the values on it are not modified). Prediction interval (on the y-axis) given from the standard score (on the x-axis).
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