Exploring the Empirical Rule

The video tutorial explains the empirical rule, which describes how data in a normal distribution is spread around the mean. It uses the example of women's heights to illustrate how the rule can be applied to real-world data. The tutorial covers calculating the percentage of women within certain height ranges and discusses the rarity of extreme heights. The empirical rule is shown to be a useful tool for understanding data distribution in various contexts.

What is the Empirical Rule primarily used to describe?

• The distribution of data in a skewed distribution

• The distribution of data in a bimodal distribution

• The distribution of data in a uniform distribution

• The distribution of data in a normal distribution

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CCSS.HSS.ID.A.4

According to the Empirical Rule, what percentage of data falls within one standard deviation of the mean?

• 99.7%

• 50%

• 68%

• 95%

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CCSS.HSS.ID.A.4

If the mean height of women is 65 inches with a standard deviation of 3 inches, what percentage of women are taller than 65 inches?

• 34%

• 50%

• 95%

• 68%

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CCSS.HSS.ID.A.4

What height range corresponds to one standard deviation from the mean if the mean height is 65 inches and the standard deviation is 3 inches?

• 62 to 68 inches

• 59 to 71 inches

• 65 to 68 inches

• 62 to 71 inches

Approximately what percentage of women fall between 62 inches and 68 inches?

• 99.7%

• 50%

• 68%

• 95%

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CCSS.HSS.ID.A.4

What is the height range for two standard deviations from the mean if the mean height is 65 inches and the standard deviation is 3 inches?

• 62 to 71 inches

• 59 to 71 inches

• 65 to 68 inches

• 62 to 68 inches

What percentage of women fall between 59 inches and 74 inches?

• 50%

• 99.7%

• 95%

• 68%

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CCSS.HSS.ID.A.4

What percentage of women are taller than 74 inches?

• 0.15%

• 34%

• 2.35%

• 13.5%

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CCSS.HSS.ID.A.4

If a woman's height is three standard deviations above the mean, what is her height in inches if the mean is 65 inches and the standard deviation is 3 inches?

• 68 inches

• 71 inches

• 77 inches

• 74 inches

What is the percentage of women who are shorter than 59 inches or taller than 74 inches?

• 5%

• 4.7%

• 2.35%

• 0.15%

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CCSS.HSS.ID.A.4