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Grade 11 · Math · Algebra 2

11th grade Z-scores and normal probabilities worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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z-scores and normal probabilities

Grade 11 Math Worksheet - Building Confidence

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  1. Dot plot of the class's values with the balance point 50 marked and one spread, 8, drawn as an arrow. Tala scores 62 on a class puzzle test with mean 50 and SD 8. What is the z-score of 62?

  2. Dot plot of the class's values with the balance point 56 marked and one spread, 5, drawn as an arrow. Ari's bean plant is 44 cm tall; the class's plants have mean 56 cm and SD 5 cm. What is the z-score of 44?

  3. Dot plot with the balance point 70 marked and one spread, 5, drawn as an arrow. Scores on Jun's class quiz have mean 70 and SD 5. What score has a z-score of 2?

  4. Paper airplanes in Kira's class fly a mean of 150 cm with SD 12 cm. What flight has a z-score of -1.5?

  5. Dot plot with the balance point 30 marked and one spread, 4, drawn as an arrow. Luz's class reads a mean of 30 pages a day with SD 4 pages. What page count has a z-score of 0.75?

  6. Milo checks a machine that fills rice bags with a mean of 500 g and SD 20 g. What fill has a z-score of -2.5?

  7. Noah's class puzzle scores are normal with mean 50 and SD 8. The z-score of 62 is 1.5. To four decimal places, what fraction of the scores are above 62?

  8. Bean plants in Pia's class have normal heights: mean 50 cm, SD 4 cm. A 44 cm plant has z = -1.5. To four decimal places, what fraction of the plants are below 44 cm?

  9. Ren's class jump heights are normal with mean 40 cm and SD 5 cm. The z-score of 51 cm is 2.2. To four decimal places, what fraction of the jumps are above 51 cm?

  10. Tala's class bike lap times are normal with mean 60 s and SD 5 s. The z-score of 56 s is -0.8. To four decimal places, what fraction of the times are below 56 s?

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11th grade Z-scores and normal probabilities worksheet – printable
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About this worksheet

Z-scores and normal probabilities. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find a z-score and turn a z-score back into a value.
  • I can read a z-table for areas above, below and between values, using symmetry for negative z.
  • I can compare results from different groups by z and find a value from a percent.

Standard: S-ID.A.4

Words to know

z-score: How many SDs a value sits from the mean; negative below it.

z-table: A list of areas to the left of each z.

symmetry: The area left of −z equals the area right of z.

relative standing: How a result compares with its own group.

percentile: The percent of values below a value.

Common mistakes

Flipped the sign of a z-score: a value below the mean has a negative z. Point to the value on a drawn curve together and say which side it is on.

Used the gap from the mean without dividing by the standard deviation.

Divided the mean by the SD before subtracting. Write the brackets in z = (value − mean) ÷ SD together.

What to say

Ask: how many SDs is that gap?

Questions parents ask

What is the most common mistake with z-scores and normal probabilities?

Flipped the sign of a z-score: a value below the mean has a negative z. Point to the value on a drawn curve together and say which side it is on.

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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