Normal Distribution Worksheet 6

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 97 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 87 and 107?

A variable is normally distributed with mean 97 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 91 and 103?

A variable is normally distributed with mean 76 and standard deviation 9. Using the 68–95–99.7 rule, approximately what percent is between 49 and 103?

A variable is normally distributed with mean 69 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 65 and 73?

A variable is normally distributed with mean 58 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 38 and 78?

A variable is normally distributed with mean 71 and standard deviation 8. Using the 68–95–99.7 rule, approximately what percent is between 47 and 95?

A variable is normally distributed with mean 79 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 76 and 82?

A variable is normally distributed with mean 94 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 74 and 114?

A variable is normally distributed with mean 69 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 60 and 78?

A variable is normally distributed with mean 68 and standard deviation 5. Using the 68–95–99.7 rule, approximately what percent is between 63 and 73?

A variable is normally distributed with mean 98 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 92 and 104?

A variable is normally distributed with mean 74 and standard deviation 9. Using the 68–95–99.7 rule, approximately what percent is between 47 and 101?

A variable is normally distributed with mean 64 and standard deviation 4. Using the 68–95–99.7 rule, approximately what percent is between 60 and 68?

A variable is normally distributed with mean 90 and standard deviation 2. Using the 68–95–99.7 rule, approximately what percent is between 86 and 94?

A variable is normally distributed with mean 94 and standard deviation 5. Using the 68–95–99.7 rule, approximately what percent is between 79 and 109?

A variable is normally distributed with mean 57 and standard deviation 5. Using the 68–95–99.7 rule, approximately what percent is between 52 and 62?

A variable is normally distributed with mean 82 and standard deviation 3. Using the 68–95–99.7 rule, approximately what percent is between 76 and 88?

A variable is normally distributed with mean 92 and standard deviation 10. Using the 68–95–99.7 rule, approximately what percent is between 62 and 122?

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 focuses on statistics, normal distribution, data analysis. It is designed for 11th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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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.