Finding Probabilities and Values from a Normal Model · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Reading the bell curve both ways

Mathematics · Probability · ages 17-18
Name ______________________   Date ____________

  1. About what percent of normal values lie within 2 standard deviations of the mean?

    • 95%
    • 68%
    • 99.7%
    • 50%

  2. A normal model has mean 60 and standard deviation 5. What is the z-score of the value 70?

    Answer: ______________

  3. A normal model has mean 60 and standard deviation 5. What is the z-score of the value 70?

    Answer: ______________

  4. A normal model has mean 50 and standard deviation 3. What is the z-score of the value 59?

    Answer: ______________

  5. IQ style scores are normal with mean 100 and standard deviation 15. Below which score do about the bottom 2.5% fall?

    • 85
    • 70
    • 55

  6. IQ style scores are normal with mean 100 and standard deviation 15. Below which score do about the bottom 2.5% fall?

    • 70
    • 85
    • 55
    • 115

  7. Exam marks are normal with mean 70 and standard deviation 4. About which mark is beaten by only the top 2.5%?

    Answer: ______________

  8. Exam marks are normal with mean 70 and standard deviation 4. About which mark is beaten by only the top 2.5%?

    Answer: ______________

  9. About what share of normal values lie more than 2 deviations above the mean?

    • 5%
    • 25%
    • 2.5%

  10. Exam marks are normal with mean 60 and standard deviation 8. About which mark is beaten by only the top 10%?

    • about 70
    • about 68
    • about 76
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Reading the bell curve both ways W1-mt_naXMRySvos-s1

  1. 95% · The empirical rule puts about 68% within 1, 95% within 2, and 99.7% within 3 standard deviations.
  2. 2 · 70 is 10 above the mean of 60, and 10 divided by the standard deviation 5 is 2.
  3. 2 · 70 is 10 above the mean, and 10 divided by 5 is 2.
  4. 3 · 59 minus 50 is 9, and 9 divided by 3 is 3.
  5. 70 · Two deviations are 30, and 100 minus 30 is 70.
  6. 70 · The bottom 2.5% lies about 2 deviations below the mean, so 100 minus 30 is 70.
  7. 78 · The top 2.5% starts about 2 deviations above the mean, so 70 plus 2 times 4 is 78.
  8. 78 · The top 2.5% starts about 2 deviations above the mean, so 70 plus 2 times 4.
  9. 2.5% · 5% fall outside 2 deviations, split evenly, so 2.5% sit above.
  10. about 70 · Top 10% has z about 1.28, so 60 + 1.28 times 8 is about 70.
Worksheet · LightMySky