Worksheets · Algebra 2

Normal distributions worksheet

A z-score says how many standard deviations a value sits from the mean. Subtract the mean, divide by the standard deviation, and the sign tells you which side you are on. Going the other way, multiply and add back.

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Sigma Prep · sigmaprep.io/worksheets

Name

Normal Distributions

Date Period

Find each value.

  1. A set is normal with mean 65 and standard deviation 8. Find the value with a z-score of 1
  2. A set is normal with mean 80 and standard deviation 12. Find the value with a z-score of 1
  3. A set is normal with mean 125 and standard deviation 5. Find the z-score of 120
  4. A set is normal with mean 90 and standard deviation 2. Find the z-score of 86
  5. A set is normal with mean 65 and standard deviation 5. Find the value with a z-score of 1
  6. A set is normal with mean 75 and standard deviation 4. Find the z-score of 63
  7. A set is normal with mean 115 and standard deviation 8. Find the z-score of 99
  8. A set is normal with mean 100 and standard deviation 8. Find the z-score of 116
  9. A set is normal with mean 90 and standard deviation 10. Find the value with a z-score of 2
  10. A set is normal with mean 110 and standard deviation 4. Find the z-score of 98
  11. A set is normal with mean 80 and standard deviation 5. Find the value with a z-score of 3
  12. A set is normal with mean 70 and standard deviation 8. Find the z-score of 54
  13. A set is normal with mean 120 and standard deviation 8. Find the value with a z-score of 2
  14. A set is normal with mean 90 and standard deviation 10. Find the value with a z-score of 2
  15. A set is normal with mean 125 and standard deviation 12. Find the value with a z-score of 2
  16. A set is normal with mean 125 and standard deviation 12. Find the z-score of 89
  17. A set is normal with mean 80 and standard deviation 12. Find the value with a z-score of 3
  18. A set is normal with mean 110 and standard deviation 12. Find the value with a z-score of 3
  19. A set is normal with mean 70 and standard deviation 12. Find the z-score of 106
  20. A set is normal with mean 70 and standard deviation 5. Find the z-score of 65

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Normal DistributionsAnswer keyVersion 1

Date Period

Find each value.

  1. A set is normal with mean 65 and standard deviation 8. Find the value with a z-score of 173
  2. A set is normal with mean 80 and standard deviation 12. Find the value with a z-score of 192
  3. A set is normal with mean 125 and standard deviation 5. Find the z-score of 1201
  4. A set is normal with mean 90 and standard deviation 2. Find the z-score of 862
  5. A set is normal with mean 65 and standard deviation 5. Find the value with a z-score of 160
  6. A set is normal with mean 75 and standard deviation 4. Find the z-score of 633
  7. A set is normal with mean 115 and standard deviation 8. Find the z-score of 992
  8. A set is normal with mean 100 and standard deviation 8. Find the z-score of 1162
  9. A set is normal with mean 90 and standard deviation 10. Find the value with a z-score of 2110
  10. A set is normal with mean 110 and standard deviation 4. Find the z-score of 983
  11. A set is normal with mean 80 and standard deviation 5. Find the value with a z-score of 365
  12. A set is normal with mean 70 and standard deviation 8. Find the z-score of 542
  13. A set is normal with mean 120 and standard deviation 8. Find the value with a z-score of 2104
  14. A set is normal with mean 90 and standard deviation 10. Find the value with a z-score of 270
  15. A set is normal with mean 125 and standard deviation 12. Find the value with a z-score of 2149
  16. A set is normal with mean 125 and standard deviation 12. Find the z-score of 893
  17. A set is normal with mean 80 and standard deviation 12. Find the value with a z-score of 3116
  18. A set is normal with mean 110 and standard deviation 12. Find the value with a z-score of 374
  19. A set is normal with mean 70 and standard deviation 12. Find the z-score of 1063
  20. A set is normal with mean 70 and standard deviation 5. Find the z-score of 651

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

A set is normal with mean 70 and standard deviation 5. Find the z-score of 80

  1. 80 minus the mean 70 is 10.
  2. 10 divided by the standard deviation 5.

The answer is 2.

Where students go wrong

Dividing by the mean instead of the standard deviation. The mean gets subtracted; the standard deviation is what you divide by.

Also called z-score, standard deviations from the mean, empirical rule or bell curve.

Questions about these worksheets

Yes. Every normal distributions sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Algebra 2 is usually taken around 10th or 11th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the normal distributions questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Dividing by the mean instead of the standard deviation. The mean gets subtracted; the standard deviation is what you divide by.