The 68–95–99.7 Rule
Use the empirical rule to estimate normal distribution probabilities quickly.
The rule
For an approximately normal distribution:
\[\mu\pm1\sigma\]about 68%
\[\mu\pm2\sigma\]about 95%
\[\mu\pm3\sigma\]about 99.7%
Worked example
Scores are approximately normal with mean \(70\) and standard deviation \(5\). Estimate the percentage of scores between 60 and 80.
Since the interval is \(\mu\pm2\sigma\), the percentage is about \(95\%\).