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.
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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%
5%
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?
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