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Grade 11 · Math · Precalculus

11th grade Binomial averages, the Central Limit Theorem and the normal curve worksheet

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Binomial averages, the Central Limit Theorem and the normal curve

Grade 11 Math Worksheet - Challenge Me

NameDate

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

  1. Kira wants P(X ≥ 60) for heads in 100 coin flips. Counts are whole numbers, so the normal curve needs a half-unit edge. What x-value marks the edge of that area?

    • 60
    • 60.5
    • 59.5

  2. Luz wants P(X ≤ 40) for blue spins out of 120. Counts are whole numbers, so the normal curve needs a half-unit edge. What x-value marks the edge of that area?

    • 39.5
    • 40
    • 40.5

  3. Milo wants P(X > 60) for sprouting seeds out of 75. Counts are whole numbers, so the normal curve needs a half-unit edge. What x-value marks the edge of that area?

    • 59.5
    • 60
    • 60.5

  4. Ren wants P(X < 40) for made shots out of 64. Counts are whole numbers, so the normal curve needs a half-unit edge. What x-value marks the edge of that area?

    • 40.5
    • 40
    • 39.5

  5. Tala spins a spinner 625 times: mean 125 reds, standard deviation 10. With the 68–95–99.7 rule, about what percent of runs give more than 145?

  6. Zee's school flips 900 coins: mean 450 heads, standard deviation 15. With the 68–95–99.7 rule, about what percent of runs give fewer than 435?

  7. Bo guesses on 100 true-false questions: mean 50 right, standard deviation 5. With the 68–95–99.7 rule, about what percent of runs give more than 55?

  8. Sunflower heights have standard deviation 20 cm. Jun wants the sample mean's standard deviation to be 4 cm. How many values should each sample have?

  9. Rice bag weights have standard deviation 30 g. Kira wants the sample mean's standard deviation to be 3 g. How many values should each sample have?

  10. Bus waits have standard deviation 9 minutes. Luz wants the sample mean's standard deviation to be 1.5 minutes. How many values should each sample have?

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11th grade Binomial averages, the Central Limit Theorem and the normal curve worksheet – printable
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About this worksheet

Binomial averages, the Central Limit Theorem and the normal curve. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the mean, variance and standard deviation of a binomial count.
  • I can find how much sample means spread and how big a sample needs to be.
  • I can use the normal curve for a binomial count: its z-score, its half-unit edge, and a tail chance from the 68–95–99.7 rule.

Standard: S-ID.A.4, S-MD.A.2 (+)

Words to know

binomial count: How many successes in n tries, each with the same chance p.

variance: The spread squared: n × p × (1 − p) for a binomial count.

standard deviation: The typical distance from the balance point; the square root of the variance.

sample mean: The average of one sample of n values.

Central Limit Theorem: Sample means pile into a bell shape with spread σ ÷ √n.

continuity correction: Moving the edge half a unit, because counts are whole numbers.

Common mistakes

Multiplied by the chance of the other outcome. Ask which outcome the question counts, then use its chance.

Used 70 for 70%. A percent is a part of 100, so 70% is 0.7.

Gave n × p, the mean, for the variance. The variance also multiplies by 1 − p.

Questions parents ask

What is the most common mistake with binomial averages, the central limit theorem and the normal curve?

Multiplied by the chance of the other outcome. Ask which outcome the question counts, then use its chance.

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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