Normal Distribution

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What is a Normal Distribution?

Back

A Normal Distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

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What is the Empirical Rule?

Back

The Empirical Rule states that for a normal distribution: about 68% of the data falls within 1 standard deviation of the mean, about 95% falls within 2 standard deviations, and about 99.7% falls within 3 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

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?

Back

95%.

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CCSS.HSS.ID.A.4

Front

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

Back

99.7%.

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CCSS.HSS.ID.A.4

Front

If the mean age of golfers is 38 and the standard deviation is 4, what is the age range for 68% of golfers?

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34 to 42 years old.

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CCSS.HSS.ID.A.4

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If the mean height of adult American men is 69 inches and the standard deviation is 2.5 inches, what height range includes approximately 95% of men?

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64 inches to 74 inches.

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CCSS.HSS.ID.A.4

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What is the mean in a normal distribution?

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The mean is the average of all data points and is the center of the normal distribution.

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CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

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What is the standard deviation in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion of a set of values.

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If the mean shelf life of a dairy product is 12 days with a standard deviation of 3 days, what percentage of products last between 12 and 15 days?

Back

34%.

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CCSS.HSS.ID.A.4