Empirical Rule

Mark the images that represent a normal probability distribution.

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CCSS.6.SP.A.3

According to the empirical rule, what is the percentage of data that falls within one standard deviation of the mean?

• 67%

• 65%

• 72%

• 68%

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CCSS.HSS.ID.A.4

Using the empirical rule, what is the percentage of data that falls within two standard deviations of the mean?

• 68%

• 99.7%

• 95%

• 98%

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CCSS.HSS.ID.A.4

What is the percentage of data that falls within three standard deviations of the mean, according to the empirical rule?

• 99.7%

• 98.7%

• 95%

• 100%

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CCSS.HSS.ID.A.4

Using the Empirical Rule:

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?

• 68%

• 34%

• 16%

• 2.5%

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CCSS.HSS.ID.A.4

Which interval shows 68% of the data given a mean of 15 and a standard deviation of 3? 

Hint: Sketch the Normal Distribution curve.

• 9 to 21

• 12 to 18

• 6 to 24

• 13 to 16

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CCSS.HSS.ID.A.4

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

2000 freshman at NC State University took a biology test. The scores were distributed normally with a mean of 70 and a standard deviation of 5. What percentage of scores are between 65 and 75?

(a)  

• 68%
• 34%
• 50%
• 99%

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CCSS.HSS.ID.A.4

500 juniors at Central High School took the ACT last year. The scores were distributed normally with a mean of 24 and standard deviation of 4. Approximately how many juniors scored between 16 and 32?

• 340

• 250

• 475

• 95

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CCSS.HSS.ID.A.4

Which of the following is a disadvantage of the Empirical Rule?

• There is no result for 4 standard deviations.

• It is very conservative.

• There is no result for 1 standard deviation.

• The data has to be approximately normal.

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CCSS.HSS.ID.A.4