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Normal Distributions & z-Scores — Easy Worksheet 2
Grade 11 · MathSheets Name: ____________________ Date: __________
Use z = (x - μ) / σ and the 68-95-99.7 rule.
How to solve
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Example
The test scores are normally distributed with mean 75 and standard deviation 6. Find the z-score of 87.
Answer: 2
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The adult heights in inches are normally distributed with mean 66 and standard deviation 3. Find the z-score of 57.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The test scores are normally distributed with mean 75 and standard deviation 6. Find the z-score of 69.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The test scores are normally distributed with mean 75 and standard deviation 6. Find the z-score of 69.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The cereal box weights in grams are normally distributed with mean 500 and standard deviation 10. Find the z-score of 470.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The test scores are normally distributed with mean 75 and standard deviation 6. Find the z-score of 63.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The test scores are normally distributed with mean 75 and standard deviation 6. Find the z-score of 81.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The test scores are normally distributed with mean 75 and standard deviation 6. Find the z-score of 87.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
✓ Correct!
Not quite. The answer is
💡 How to solve: Normal Distributions & z-Scores
A z-score, z = (x - μ) ÷ σ, tells how many standard deviations a value is from the mean. In a normal distribution about 68% of the data is within 1 standard deviation of the mean, 95% within 2 and 99.7% within 3. On each side of the mean that gives bands of 34%, 13.5%, 2.35% and 0.15%.
Try a similar one
The test scores are normally distributed with mean 70 and standard deviation 8. Find the z-score of 46.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Normal Distributions & z-Scores — Easy Worksheet 2
Use z = (x - μ) / σ and the 68-95-99.7 rule.