Normal Distribution Worksheet 8

Use combinations, ordered arrangements and explicitly approximate normal-distribution rules.

hard: Use another set to practice explaining and checking your answers.

23 problems · 20-25 minutes · Skills: statistics, normal distribution, data analysis

About This Worksheet

This hard-level worksheet contains 23 problems designed for 11th Grade students practicing normal distribution. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Factor polynomials, use exponent laws and solve equations with domain restrictions.

Use combinations, ordered arrangements and explicitly approximate normal-distribution rules.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: 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?

Solution Steps:

The bounds are 1 standard deviation(s) from the mean.
The empirical rule gives approximately 68% in that interval.

Answer: Approximately 68%

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

A variable is normally distributed with mean 65 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 55 and 75?

A variable is normally distributed with mean 90 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 70 and 110?

A variable is normally distributed with mean 71 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 62 and 80?

A variable is normally distributed with mean 92 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 88 and 96?

A variable is normally distributed with mean 89 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 73 and 105?

A variable is normally distributed with mean 88 and standard deviation 9. Using the 68–95–99.7 rule, approximately what percent is between 61 and 115?

A variable is normally distributed with mean 89 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 81 and 97?

A variable is normally distributed with mean 52 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 44 and 60?

A variable is normally distributed with mean 58 and standard deviation 2. Using the 68–95–99.7 rule, approximately what percent is between 52 and 64?

A variable is normally distributed with mean 58 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 50 and 66?

A variable is normally distributed with mean 53 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 45 and 61?

A variable is normally distributed with mean 63 and standard deviation 5. Using the 68–95–99.7 rule, approximately what percent is between 48 and 78?

A variable is normally distributed with mean 84 and standard deviation 2. Using the 68–95–99.7 rule, approximately what percent is between 82 and 86?

A variable is normally distributed with mean 69 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 49 and 89?

A variable is normally distributed with mean 74 and standard deviation 7. Using the 68–95–99.7 rule, approximately what percent is between 53 and 95?

A variable is normally distributed with mean 57 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 49 and 65?

A variable is normally distributed with mean 54 and standard deviation 7. Using the 68–95–99.7 rule, approximately what percent is between 40 and 68?

A variable is normally distributed with mean 59 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 29 and 89?

A variable is normally distributed with mean 80 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 74 and 86?

A variable is normally distributed with mean 98 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 86 and 110?

A variable is normally distributed with mean 71 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 53 and 89?

A variable is normally distributed with mean 63 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 57 and 69?

A variable is normally distributed with mean 97 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 89 and 105?

Answer Key

1. Approximately 68%2. Approximately 95%3. Approximately 99.7%4. Approximately 68%5. Approximately 95%6. Approximately 99.7%7. Approximately 68%8. Approximately 95%9. Approximately 99.7%10. Approximately 68%11. Approximately 95%12. Approximately 99.7%13. Approximately 68%14. Approximately 95%15. Approximately 99.7%16. Approximately 68%17. Approximately 95%18. Approximately 99.7%19. Approximately 68%20. Approximately 95%21. Approximately 99.7%22. Approximately 68%23. Approximately 95%

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