Normal Distribution Worksheets
Use combinations, ordered arrangements and explicitly approximate normal-distribution rules.
Before you begin
Factor polynomials, use exponent laws and solve equations with domain restrictions.
Worked example
A variable is normally distributed with mean 65 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 62 and 68?
- The bounds are 1 standard deviation(s) from the mean.
- The empirical rule gives approximately 68% in that interval.
Answer: Approximately 68%
Check your result using the method in the example before moving to the next question.
Choose your level
These sets use the same exercise types and number ranges across level labels. Choose a fresh set for additional practice.
- Easy: Start with the preview and follow the worked example.
- Medium: Practice the same exercise types with a fresh numbered set.
- Hard: Use another set to practice explaining and checking your answers.
Questions and answer calculations checked on 2026-09-17. How we check worksheets. Free for personal and classroom use.
Preview and print an easy set
Try six questions below, or choose a full set at your level.
1
A variable is normally distributed with mean 75 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 67 and 83?
2
A variable is normally distributed with mean 89 and standard deviation 7. Using the 68–95–99.7 rule, approximately what percent is between 75 and 103?
3
A variable is normally distributed with mean 62 and standard deviation 5. Using the 68–95–99.7 rule, approximately what percent is between 47 and 77?
4
A variable is normally distributed with mean 61 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 51 and 71?
5
A variable is normally distributed with mean 84 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 72 and 96?
6
A variable is normally distributed with mean 53 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 41 and 65?
Answer Key
1. Approximately 68%2. Approximately 95%3. Approximately 99.7%4. Approximately 68%5. Approximately 95%6. Approximately 99.7%