The 68-95-99.7 Rule Captures Almost Every Measurement on a Bell Curve
In any Gaussian normal distribution, 68% of data sits within 1 standard deviation, 95% within 2, and a massive 99.7% within 3.
📊 Bell Curve
NIST Engineering Statistics Handbook
On a normal bell curve, roughly what % of observations lie within ±2 standard deviations?
Each standard deviation (sigma) out on the bell curve shrinks tail failure rates dramatically.
📊 Statistics
Bell Curve
Why / How?
Scientific Mechanism
Formalized by Carl Friedrich Gauss, the normal distribution lets engineers quantify how extreme an outlier truly is. Moving just a few standard deviations (sigma) away from the mean makes rare errors drop exponentially—which is why 'Six Sigma' quality programs target fewer than 3.4 defects per million.
Why It Matters
Each standard deviation (sigma) out on the bell curve shrinks tail failure rates dramatically.
