Normal Distribution and Empirical Rule Worksheet

According to the empirical rule, what percentage of data falls within 1 standard deviation? 

• 25%

• 68%

• 95%

• 99.7%

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CCSS.HSS.ID.A.4

In a factory, the weight of the concrete poured into a mold by a machine follows a normal distribution with a mean of 1150 pounds and a standard deviation of 22 pounds. Approximately 95% of molds filled by this machine will hold weights in what interval?

• 1084 to 1216 pounds 

• 1106 to 1150 pounds 

• 1106 to 1194 pounds 

• 1128 to 1172 pounds

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CCSS.HSS.ID.A.4

At a local high school, GPA's are normally distributed with a mean of 2.9 and standard deviation of 0.6. What percentage of students at the high school have a GPA between 2.3 and 3.5?

• 68%

• 99.7%

• 95%

• 84%

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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?

• 68%

• 34%

• 16%

• 2.5%

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CCSS.HSS.ID.A.4

When Avani goes bowling, her scores are normally distributed with a mean of 145 and a standard deviation of 12. Using the empirical rule, determine the interval that would represent the middle 68% of the scores of all the games that Avani bowls.

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CCSS.HSS.ID.A.4

A town's average snowfall is 48 inches per year with a standard deviation of 6 inches. Using a Normal model, what percent of snowfall amounts will be between 40 and 50?

• 0.5393

• 0.4607

• 0.3719

• 0.7234

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CCSS.HSS.ID.A.4

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score between 68 and 82

• 11

• 2

• 340

• 498

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CCSS.HSS.ID.A.4

When Julia goes bowling, her scores are normally distributed with a mean of 200 and a standard deviation of 14. Using the empirical rule, what percentage of the games that Julia bowls does she score between 158 and 242?

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CCSS.HSS.ID.A.4

Scores on a certain standardized test have a mean of 500, and a standard deviation of 100. How common is a score between 600 and 700? Calculate the probability. 

• 2.5%

• 2.35%

• 16%

• 13.5%

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CCSS.HSS.ID.A.4

Given a mean of 75 and a standard deviation of 7, how many students out of 500 would score higher than 68?

• 11

• 12

• 420

• 250

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CCSS.HSS.ID.A.4