Normal Distribution Worksheet 5

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

medium: Practice the same exercise types with a fresh numbered set.

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

About This Worksheet

This medium-level worksheet contains 18 problems designed for 11th Grade students practicing normal distribution. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

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 62 and standard deviation 9. Using the 68–95–99.7 rule, approximately what percent is between 53 and 71?

A variable is normally distributed with mean 75 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 69 and 81?

A variable is normally distributed with mean 53 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 44 and 62?

A variable is normally distributed with mean 57 and standard deviation 9. Using the 68–95–99.7 rule, approximately what percent is between 48 and 66?

A variable is normally distributed with mean 94 and standard deviation 2. Using the 68–95–99.7 rule, approximately what percent is between 90 and 98?

A variable is normally distributed with mean 88 and standard deviation 7. Using the 68–95–99.7 rule, approximately what percent is between 67 and 109?

A variable is normally distributed with mean 99 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 93 and 105?

A variable is normally distributed with mean 64 and standard deviation 9. Using the 68–95–99.7 rule, approximately what percent is between 46 and 82?

A variable is normally distributed with mean 99 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 87 and 111?

A variable is normally distributed with mean 73 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 69 and 77?

A variable is normally distributed with mean 70 and standard deviation 7. Using the 68–95–99.7 rule, approximately what percent is between 56 and 84?

A variable is normally distributed with mean 54 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 45 and 63?

A variable is normally distributed with mean 55 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 49 and 61?

A variable is normally distributed with mean 50 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 34 and 66?

A variable is normally distributed with mean 78 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 54 and 102?

A variable is normally distributed with mean 57 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 53 and 61?

A variable is normally distributed with mean 96 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 76 and 116?

A variable is normally distributed with mean 57 and standard deviation 6. Using the 68–95–99.7 rule, approximately what percent is between 39 and 75?

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%

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This worksheet contains 18 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.