Empirical Rule Worksheet

Explore the Empirical Rule (68-95-99.7 rule) with this grade 6 math worksheet, featuring questions on data distribution and percentages within standard deviations.

Grade 6 Math Probability and StatisticsEmpirical Rule

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2 Short AnswerFill in the BlanksTextMultiple Choice

Standards

CCSS.MATH.CONTENT.6.SP.A.2CCSS.MATH.CONTENT.6.SP.B.5.C

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Empirical Rule Worksheet

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Read each question carefully and answer based on your understanding of the Empirical Rule (68-95-99.7 rule).

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

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

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

4. If a dataset has a mean of 50 and a standard deviation of 5, then approximately 68% of the data will fall between and .

5. For the same dataset (mean=50, standard deviation=5), approximately 95% of the data will fall between and .

6. For the same dataset (mean=50, standard deviation=5), approximately 99.7% of the data will fall between and .

Use the diagram below to help answer the next questions.

7. For a normal distribution, what percentage of data falls outside of one standard deviation from the mean?

32%

0.3%

68%

8. What percentage of data falls between one and two standard deviations above the mean?

13.5%

34%

2.35%

47.5%

9. The average height of students in a class is 140 cm with a standard deviation of 5 cm. Assuming the heights are normally distributed, what percentage of students are between 135 cm and 145 cm tall?

10. A factory produces light bulbs with a mean lifespan of 1000 hours and a standard deviation of 50 hours. What percentage of light bulbs are expected to last between 900 hours and 1100 hours?