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

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

Phone batteries last a mean of 40 hours, with standard deviation 12 hours. Esme averages samples of 36. What is the standard deviation of the sample mean, in hours?
Sunflowers in a field average 150 cm tall, with standard deviation 20 cm. Jun averages samples of 25. What is the standard deviation of the sample mean, in cm?
Bags of rice average 500 g, with standard deviation 30 g. Luz averages samples of 100. What is the standard deviation of the sample mean, in g?
Phone batteries last a mean of 40 hours (standard deviation 12). A sample of 36 averages 43 hours. Milo compares it with the balance point. What is the z-score of this sample mean?
Sunflowers average 150 cm (standard deviation 20). A sample of 25 averages 142 cm. Ren compares it with the balance point. What is the z-score of this sample mean?
Bus waits average 12 minutes (standard deviation 6). A sample of 16 waits averages 15 minutes. Tala compares it with the balance point. What is the z-score of this sample mean?
Rice bags average 500 g (standard deviation 30). A sample of 100 bags averages 494 g. Zee compares it with the balance point. What is the z-score of this sample mean?
Ari flips a fair coin 100 times and gets 60 heads. With n = 100 and p = 0.5, and the normal curve for the count, what is the z-score of 60?
Bo's class flips 400 coins and gets 190 heads. With n = 400 and p = 0.5, and the normal curve for the count, what is the z-score of 190?
Jun's school flips 900 coins and gets 495 heads. With n = 900 and p = 0.5, and the normal curve for the count, what is the z-score of 495?

11th grade Binomial averages, the Central Limit Theorem and the normal curve worksheet – printable — Print: 1 2 3 4 5 6

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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