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Grade 11 · Math · Algebra 2

11th grade The normal curve and the empirical rule worksheet

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The normal curve and the empirical rule

Grade 11 Math Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

  1. The middle 68% of the times for Ren's class to tie a knot lie between 61 and 69 seconds. The data are roughly normal. What is the standard deviation?

  2. Nearly all, 99.7%, of the eggs Tala weighs at a farm lie between 44 g and 80 g. The data are roughly normal. What is the standard deviation?

  3. The middle 95% of the minutes Zee's classmates read each week lie between 140 and 180 minutes. The data are roughly normal. What is the standard deviation?

  4. Scores in Ari's class quiz game are roughly normal, with mean 60 and SD 8. Only 2.5% of scores are above which score?

  5. Normal curve with its mean 120 marked and one SD, 6, drawn as an arrow from the mean. The heights of the sunflowers at Bo's school are roughly normal, with mean 120 cm and SD 6 cm. About 16% of heights are below which height?

  6. The hours the flashlights in Jun's class run are roughly normal, with mean 9 and SD 0.5. Only 0.15% of run times are above which time?

  7. Kira compares two classes' run times; both are normal with mean 60 s. Which class has the larger percent of times above 70 s?

    • Class A: its taller curve holds more of the values
    • Class A: 16%, against 2.5%
    • The same percent, because the means are equal
    • Class B: 16%, against 2.5%

  8. Luz compares two machines filling juice bottles; both fills are normal with mean 500 mL. Which machine fills the larger percent of bottles below 496 mL?

    • Machine B: 16%, against 2.5%
    • Machine A: 16%, against 2.5%
    • The same percent, because the means are equal
    • Machine A: its taller curve holds more of the values

  9. Milo compares two groups' plant heights; both are normal with mean 50 cm. Which group has the larger percent between 44 and 56 cm?

    • Group B: its wider curve covers more of the line
    • The same percent, because the means are equal
    • Group A: 99.7%, against 68%
    • Group B: 99.7%, against 68%

  10. Noah compares two teams' jump heights; both are normal with mean 100 cm. Which team has the larger percent between 90 and 110 cm?

    • Team A: 95%, against 68%
    • Team B: its wider curve covers more of the line
    • Team B: 95%, against 68%
    • The same percent, because the means are equal
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11th grade The normal curve and the empirical rule worksheet – printable
Print: 123456

About this worksheet

The normal curve and the empirical rule. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can use the 68-95-99.7 rule for percents between, above and below values.
  • I can find a value from a percent, and an SD from a band.
  • I can tell a skewed shape from a symmetric one and say where the mean sits.

Standard: S-ID.A.4

Words to know

normal curve: A smooth, symmetric hill: the dot plot smoothed.

empirical rule: 68%, 95%, 99.7% of values within 1, 2, 3 SDs.

half-band: One side of a band: 34, 13.5, 2.35 or 0.15 percent.

tail: The thin end of a curve far from the mean.

skewed right: A long tail to the right; the mean is pulled right.

Common mistakes

Used 68% (or 95%) for only one side of the mean, though that band covers both sides. Draw the curve together and shade each side.

Gave the percent on the wrong side of a value (below for above). Shade the asked part of the curve together first.

Used an amount that covers both sides of the mean (such as the 32% outside 68%) for one side. Split it in half together.

Questions parents ask

What is the most common mistake with the normal curve and the empirical rule?

Used 68% (or 95%) for only one side of the mean, though that band covers both sides. Draw the curve together and shade each side.

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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