Empirical Rule Worksheet

A Grade 12 Math worksheet on the Empirical Rule, covering its application to normal distributions and calculating probabilities within standard deviations.

Grade 12 Math Probability and StatisticsEmpirical Rule

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2 Short AnswerFill in the BlanksMultiple ChoiceCustom

Standards

CCSS.MATH.CONTENT.HSS.ID.A.4

Topics

Empirical RuleNormal DistributionStatisticsProbabilityGrade 12 Math

7 sections · Free to use · Printable

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Empirical Rule Worksheet

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Read each question carefully and answer to the best of your ability. Show all work where applicable. Remember the Empirical Rule states that for a normal distribution, approximately 68% of the data falls within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.

1. What percentage of data in a normal distribution falls within 1 standard deviation of the mean?

2. What percentage of data in a normal distribution falls within 2 standard deviations of the mean?

3. What percentage of data in a normal distribution falls within 3 standard deviations of the mean?

For a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5:

4. Approximately 68% of the data will fall between and .

5. Approximately 95% of the data will fall between and .

6. Approximately 99.7% of the data will fall between and .

7. The scores on a standardized test are normally distributed with a mean of 70 and a standard deviation of 5. What percentage of students scored between 65 and 75?

34%

68%

95%

99.7%

8. A dataset is normally distributed with a mean of 100 and a standard deviation of 10. Approximately what percentage of the data lies above 120?

2.5%

16%

32%

9. The average height of adult males in a certain city is 69 inches with a standard deviation of 2.5 inches. Assuming the heights are normally distributed, what percentage of adult males are between 64 inches and 74 inches tall?

10. A company manufactures light bulbs with a mean lifespan of 1000 hours and a standard deviation of 50 hours. If the lifespan of the bulbs is normally distributed, how many bulbs in a batch of 10,000 would you expect to last longer than 1050 hours?

11. Draw a normal distribution curve and label the mean and the points representing 1, 2, and 3 standard deviations from the mean. Shade the area that represents 95% of the data.