Empirical Rule - Shaded

Front

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, 95% falls within two standard deviations, and 99.7% falls within three standard deviations.

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CCSS.HSS.ID.A.4

Front

What percentage of data is in the shaded region within one standard deviation of the mean?

Back

68%

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CCSS.HSS.ID.A.4

Front

What percentage of data is in the shaded region within two standard deviations of the mean?

Back

95%

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CCSS.HSS.ID.A.4

Front

What percentage of data is in the shaded region within three standard deviations of the mean?

Back

99.7%

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CCSS.HSS.ID.A.4

Front

If 16% of the data is in the shaded region, how many standard deviations from the mean does this represent?

Back

This represents approximately 2 standard deviations from the mean.

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CCSS.HSS.ID.A.4

Front

If 32% of the data is in the shaded region, how many standard deviations from the mean does this represent?

Back

This represents approximately 1 standard deviation from the mean.

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CCSS.HSS.ID.A.4

Front

What percentage of data is in the shaded region if 50% is to the left of the mean?

Back

50% of the data is in the shaded region.

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CCSS.HSS.ID.A.4

Front

What percentage of data is in the shaded region if 2.5% is in the tail beyond three standard deviations?

Back

2.5% of the data is in the shaded region beyond three standard deviations.

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CCSS.HSS.ID.A.4

Front

What is the significance of the 84% in a normal distribution?

Back

84% of the data falls below one standard deviation above the mean.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the percentage of data in a shaded region for a normal distribution?

Back

Use the Empirical Rule or Z-scores to determine the area under the curve.

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CCSS.HSS.ID.A.4