Empirical Rule

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What is the Empirical Rule?

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The Empirical Rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

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Approximately 68%.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

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Approximately 95%.

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CCSS.HSS.ID.A.4

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What percentage of data falls within 3 standard deviations of the mean in a normal distribution?

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Approximately 99.7%.

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CCSS.HSS.ID.A.4

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What percentage of data is between -1 and 1 standard deviations from the mean?

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Approximately 68%.

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CCSS.HSS.ID.A.4

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What percentage of data is between -2 and -1 standard deviations from the mean?

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Approximately 13.5%.

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CCSS.HSS.ID.A.4

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What percentage of data is between 1 and 2 standard deviations from the mean?

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Approximately 13.5%.

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CCSS.HSS.ID.A.4

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What percentage of data is between -3 and -2 standard deviations from the mean?

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Approximately 2.35%.

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CCSS.HSS.ID.A.4

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What percentage of data is greater than 3 standard deviations from the mean?

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Approximately 0.15%.

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CCSS.HSS.ID.A.4

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What is the area under the normal curve between -1 and 0 standard deviations?

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Approximately 34%.

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CCSS.HSS.ID.A.4