Normal Distribution and Empirical Rule Worksheet

The Empirical (68-95-99.7) Rule can be applied only if data is ....

• Normally Distributed

• Uniform

• Skewed

• Symmetric

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CCSS.HSS.ID.A.4

What percentage of dogs weigh less than 58 pounds? Explain how you arrived at your answer.

(a)  

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What percentage of dogs weigh between 34 and 58 pounds? Explain how you arrived at your answer.

(a)  

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CCSS.HSS.ID.A.4

What percent of a normal distribution lies outside of ±3 standard deviations?

• 99.7%

• .15%

• .3%

• 100%

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Which interval shows 95% of the data given a mean of 15 and a standard deviation of 3? 

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

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CCSS.HSS.ID.A.4

This data is normally distributed. What percent of the data is in the shaded region?

• 68%

• 32%

• 16%

• 50%

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This data is normally distributed. What percent of the data is in the shaded regions?

• 5%

• 95%

• 2.5%

• 50%

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CCSS.HSS.ID.A.4

The shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. About what percent of the products last between 12 and 15 days?

(Remember to draw a curve with the values to help you.)

• 68%

• 34%

• 16%

• 2.5%

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CCSS.HSS.ID.A.4

If this is the graph of data normally distributed with a mean of 30 and a standard deviation of 5, what label (number) is written at the blue circle?

• 20

• 15

• 40

• 30

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Find the z-score for 75 given a mean of 60 and a standard deviation of 6.

• -2.5

• 2.5

• -1.15

• 1.15