Empirical Rule Worksheet

Empirical Rule Practice

Read each question carefully and use your knowledge of the Empirical Rule (68-95-99.7 rule) to answer. Show your work where applicable.

The Empirical Rule, also known as the 68-95-99.7 rule, describes how data is distributed in a normal distribution. For data that follows a normal distribution:

• Approximately 68% of the data falls within one standard deviation of the mean. • Approximately 95% of the data falls within two standard deviations of the mean. • Approximately 99.7% of the data falls within three standard deviations of the mean.

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

2. If a dataset has a mean of 100 and a standard deviation of 10, what range contains approximately 95% of the data?

3. The Empirical Rule is also known as the   rule.

4. Approximately 99.7% of the data in a normal distribution falls within   standard deviations of the mean.

5. A set of test scores are normally distributed with a mean of 75 and a standard deviation of 5. Between what two scores would you expect to find approximately 68% of the students?

6. Explain in your own words what the 'standard deviation' represents in the context of the Empirical Rule.

7. Consider a normal distribution with a mean of 50 and a standard deviation of 5. Label the number line below to show the ranges for 1, 2, and 3 standard deviations from the mean.

8. The Empirical Rule applies to all types of data distributions.

9. If 99.7% of data falls between 20 and 80, the mean of the data is 50.