<P> In statistics, the 68--95--99.7 rule is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, respectively; more accurately, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively . In mathematical notation, these facts can be expressed as follows, where X is an observation from a normally distributed random variable, μ is the mean of the distribution, and σ is its standard deviation: </P> <Dl> <Dd> Pr (μ − σ ≤ X ≤ μ + σ) ≈ 0.6827 Pr (μ − 2 σ ≤ X ≤ μ + 2 σ) ≈ 0.9545 Pr (μ − 3 σ ≤ X ≤ μ + 3 σ) ≈ 0.9974 (\ displaystyle (\ begin (aligned) \ Pr (\ mu - \; \, \ sigma \ leq X \ leq \ mu + \; \, \ sigma) & \ approx 0.6827 \ \ \ Pr (\ mu - 2 \ sigma \ leq X \ leq \ mu + 2 \ sigma) & \ approx 0.9545 \ \ \ Pr (\ mu - 3 \ sigma \ leq X \ leq \ mu + 3 \ sigma) & \ approx 0.9974 \ end (aligned))) </Dd> </Dl>

For a normal distribution two standard deviation on each side of the mean would include what
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