<Dl> <Dd> Pr (μ − 2 σ ≤ X ≤ μ + 2 σ) = Φ (2) − Φ (− 2) ≈ 0.9772 − (1 − 0.9772) ≈ 0.9545 (\ displaystyle \ Pr (\ mu - 2 \ sigma \ leq X \ leq \ mu + 2 \ sigma) = \ Phi (2) - \ Phi (- 2) \ approx 0.9772 - (1 - 0.9772) \ approx 0.9545) </Dd> </Dl> <Dd> Pr (μ − 2 σ ≤ X ≤ μ + 2 σ) = Φ (2) − Φ (− 2) ≈ 0.9772 − (1 − 0.9772) ≈ 0.9545 (\ displaystyle \ Pr (\ mu - 2 \ sigma \ leq X \ leq \ mu + 2 \ sigma) = \ Phi (2) - \ Phi (- 2) \ approx 0.9772 - (1 - 0.9772) \ approx 0.9545) </Dd> <P> This is related to confidence interval as used in statistics: X _̄ ± 2 σ n (\ displaystyle (\ bar (X)) \ pm 2 (\ frac (\ sigma) (\ sqrt (n)))) is approximately a 95% confidence interval when X _̄ (\ displaystyle (\ bar (X))) is the average of a sample of size n (\ displaystyle n). </P> <P> The "68--95--99.7 rule" is often used to quickly get a rough probability estimate of something, given its standard deviation, if the population is assumed to be normal . It is also as a simple test for outliers if the population is assumed normal, and as a normality test if the population is potentially not normal . </P>

About what percent of normally-distributed data lie within 2 standard deviations of the mean