MAKE IT YOURS

A world for every learner

Choose a grade to discover its colours and creative world.

Grade 11 Standard Deviation, z-Scores & the Normal Curve Worksheet with Answers

Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math

Unit 7: StatisticsNormal DistributionsCCSS S-ID.A.4

Measuring spread with standard deviation, standardizing with z-scores and using the 68-95-99.7 rule. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

Save to PinterestJump to answer key
  • Answer keys checked by code
  • No ads, ever
  • No student accounts needed
  • Safety & privacy
Practice Sheetaethelsystems.com

Standard Deviation, z-Scores & the Normal Curve

Grade 11 · Math

Score___ / 12

Name

Class

Date

Learning goal: Normal Distributions · CCSS S-ID.A.4

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Test scores have mean 50 and standard deviation 3. What is the z-score of a score of 41?

Answer: -3

RememberNormal distribution and counting

−3σ−2σ−1σμ+1σ+2σ+3σ68% within 1σ95% within 2σ99.7% within 3σz = (x − μ) ÷ σnPr = n! ÷ (n − r)! (order matters)nCr = n! ÷ (r!(n − r)!)
  1. 1

    Test scores have mean 100 and standard deviation 6. What is the z-score of a score of 85?

    Show your work
    Answer
  2. 2

    In a normal distribution, about what percent of data lies within 2 standard deviations of the mean?

    Show your work
    Answer
  3. 3

    Heights have mean 90 cm and standard deviation 4 cm. What height has a z-score of 0?

    Show your work
    Answer
  4. 4

    Test scores have mean 75 and standard deviation 4. What is the z-score of a score of 75?

    Show your work
    Answer
  5. 5

    In a normal distribution, about what percent of data lies within 1 standard deviation of the mean?

    Show your work
    Answer
  6. 6

    In a normal distribution, about what percent of data lies within 3 standard deviations of the mean?

    Show your work
    Answer
  7. 7

    Test scores have mean 40 and standard deviation 6. What is the z-score of a score of 22?

    Show your work
    Answer
  8. 8

    Heights have mean 55 cm and standard deviation 7 cm. What height has a z-score of 1?

    Show your work
    Answer
  9. 9

    Test scores have mean 60 and standard deviation 2. What is the z-score of a score of 55?

    Show your work
    Answer
  10. 10

    Heights have mean 35 cm and standard deviation 10 cm. What height has a z-score of 0.5?

    Show your work
    Answer
  11. 11

    Test scores have mean 90 and standard deviation 10. What is the z-score of a score of 65?

    Show your work
    Answer
  12. 12

    Heights have mean 75 cm and standard deviation 2 cm. What height has a z-score of -3?

    Show your work
    Answer

★ Challenge corner for fast finishers

On a grid, you walk from the bottom-left corner to a point 4 blocks right and 2 blocks up, moving only right or up. How many different shortest paths are there?

How did I do?

Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/std_dev_zscore

Answer key (click to show)
  1. 1.-2.5
  2. 2.95%
  3. 3.90 cm
  4. 4.0
  5. 5.68%
  6. 6.99.7%
  7. 7.-3
  8. 8.62 cm
  9. 9.-2.5
  10. 10.40 cm
  11. 11.-2.5
  12. 12.69 cm
  13. ★15 (challenge corner)

Need another Standard Deviation, z-Scores & the Normal Curve worksheet?

Generate unlimited fresh versions at easy, medium or hard difficulty, each with its own answer key. Free during our launch — no card needed.

Create a free account

How to use this worksheet

  • Use it for revision before a test, as homework, or as a timed practice set.
  • Students can self-mark with the answer key and note which question types they got wrong.
  • Generate several versions of the same topic for spaced practice in the weeks before an exam.

Related worksheets

More Grade 11 Math worksheets

Grade 11 Mean, Median & ModeGrade 11 Range & Data SpreadGrade 11 Statistics (Mixed Practice)Grade 11 Function Operations & CompositionGrade 11 Inverse FunctionsGrade 11 Transforming FunctionsGrade 11 Quadratic Formula & VertexGrade 11 Completing the Square

Can't find what you need? Tell us which worksheet to make next.

Frequently asked questions

Does this Grade 11 Standard Deviation, z-Scores & the Normal Curve worksheet come with answers?

Yes. The full answer key is on this page, and it prints on its own page after the questions. Every answer is calculated or checked by code rather than written by an AI model, so the key is always correct.

How do I print it or save it as a PDF?

Click "Download PDF" to save a ready-to-print PDF with the answer key on the last page, or click "Print" to send the worksheet and answer key straight to your printer.

Can I get a different Standard Deviation, z-Scores & the Normal Curve worksheet?

Yes. Create a free account to generate as many fresh Grade 11 Standard Deviation, z-Scores & the Normal Curve worksheets as you like, at easy, medium or hard difficulty, each with its own answer key.

Is this worksheet free?

Yes. This worksheet is free to print, and Practice Sheet is free to use during our launch with no card needed.