68-95-99.7 Rule (Empirical Rule)

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What is the 68-95-99.7 Rule?

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The 68-95-99.7 Rule, also known as the Empirical Rule, states that for a normal distribution: 68% of 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 one standard deviation of the mean in a normal distribution?

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68% of the data falls within one standard deviation of the mean.

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CCSS.HSS.ID.A.4

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

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95% of the data falls within two standard deviations of the mean.

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CCSS.HSS.ID.A.4

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

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99.7% of the data falls within three standard deviations of the mean.

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CCSS.HSS.ID.A.4

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If a GPA is normally distributed with a mean of 2.9 and a standard deviation of 0.6, what percentage of students have a GPA between 2.3 and 3.5?

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68% of students have a GPA between 2.3 and 3.5.

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CCSS.HSS.ID.A.4

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In a normal distribution, what does it mean if data is one standard deviation above the mean?

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It means that the data point is greater than the mean by the amount of the standard deviation, indicating it is higher than approximately 68% of the data.

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CCSS.HSS.ID.A.4

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For a machine producing components with lengths normally distributed, if 99.7% of components are between 1.176 cm and 1.224 cm, what are the mean and standard deviation?

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Mean = 1.200 cm, Standard Deviation = 0.008 cm.

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CCSS.HSS.ID.A.4

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What is the interval that contains approximately 95% of the weights filled by a machine with a mean of 1150 pounds and a standard deviation of 22 pounds?

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The interval is 1106 to 1194 pounds.

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CCSS.HSS.ID.A.4

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What does it mean if a data point is more than two standard deviations above the mean in a normal distribution?

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It indicates that the data point is higher than approximately 97.5% of the data.

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CCSS.HSS.ID.A.4

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How do you calculate the range for 95% of data in a normal distribution?

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The range is calculated as: Mean ± 2(Standard Deviation).

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