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Normal Distribution โ€” The 68-95-99.7 Empirical Rule

A bar graph shows numbers as bars. Taller bar = bigger number.

StatisticsCommon Core SP-2.AEDAVerified correct โœ“

Worked examples

Scores on a standardized test are normally distributed with mean ฮผ = 133 and standard deviation ฯƒ = 10. Using the 68-95-99.7 rule, what percentage of scores fall between 103 and 163?
Answer: 99.7
Scores on a standardized test are normally distributed with mean ฮผ = 156 and standard deviation ฯƒ = 5. Using the 68-95-99.7 rule, what percentage of scores fall between 151 and 161?
Answer: 68

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Standardized Scores (z-scores) โ€” Position Within a DistributionNormal Distribution โ€” Properties and z-Scores

More Statistics topics

Frequency Tables โ€” Relative Frequency and Marginal DistributionsCompare Distributions โ€” Shape, Center, Spread, and Outliers (SOCS)Dot Plots and Histograms โ€” Construct and InterpretBoxplots and the Five-Number SummaryMean and Standard Deviation โ€” Compute and InterpretStandardized Scores (z-scores) โ€” Position Within a DistributionNormal Probability Calculations Using z-tablesFind Values from Percentiles โ€” Inverse Normal