Empirical Rule

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What is the Empirical Rule?

Back

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

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CCSS.HSS.ID.A.4

Front

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

Back

Approximately 68%.

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

Back

Approximately 95%.

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

Back

Approximately 99.7%.

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CCSS.HSS.ID.A.4

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If the mean weight of concrete is 1150 pounds and the standard deviation is 22 pounds, what is the weight range for approximately 95% of molds?

Back

The weight range is approximately 1106 to 1194 pounds.

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CCSS.HSS.ID.A.4

Front

What is the weight range for approximately 68% of molds if the mean is 1150 pounds and the standard deviation is 22 pounds?

Back

The weight range is approximately 1128 to 1172 pounds.

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CCSS.HSS.ID.A.4

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What is the area under the normal distribution curve 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 is the area under the normal distribution curve between the mean and 1 standard deviation?

Back

Approximately 34%.

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CCSS.HSS.ID.A.4

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In a normal distribution, what does it mean if a data point is more than 2 standard deviations away from the mean?

Back

It indicates that the data point is in the tail of the distribution and is less common.

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CCSS.HSS.ID.A.4

Front

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

Back

Use the formula: Mean ± 2(Standard Deviation). For example, with a mean of 1150 and a standard deviation of 22, the interval is 1150 ± 2(22) = 1106 to 1194.

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