Unit 4: Statistics and Probability
Topic 4.15: Central limit theorem (HL only) Questions
Practice 12 exam-style questions for IB Math AI SL Topic 4.15. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
A population has σ = 30. For a sample of size n = 36, the standard error of the mean is:
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2026
A machine produces rods with mean length μ = 20 cm and standard deviation σ = 0.6 cm. A sample of n = 36 rods is taken and the mean length X̄ recorded. Find the standard error of X̄.
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2026
The Central Limit Theorem mainly concerns the distribution of:
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2026
Light bulbs have lifetime mean μ = 1200 h and standard deviation σ = 150 h (the distribution is skewed). A sample of n = 100 bulbs is tested. Using the central limit theorem, find P(X̄ > 1225), where X̄ is the sample mean lifetime.
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2026
A coffee chain fills cups with mean μ = 350 mL and standard deviation σ = 14 mL. A barista pours n = 49 cups.
(a) Find the standard error of the sample mean.
(b) Find the probability that the sample mean exceeds 353 mL.
(a) Find the standard error of the sample mean.
(b) Find the probability that the sample mean exceeds 353 mL.
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2026
Find the mean and standard deviation of the sample mean.
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2026
A population is NOT Normal. For the sample mean to be approximately Normal by the CLT, you need:
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2026
Explain why the central limit theorem lets you use a Normal distribution for the mean delivery time of 50 parcels, even though individual delivery times are strongly right-skewed.
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2026
Daily customer counts at a shop have mean μ = 240 and standard deviation σ = 50. Over n = 25 days the mean daily count X̄ is found. Find P(230 < X̄ < 250).
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2026
If the sample size n is multiplied by 4, the standard error of the sample mean is:
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2026
Single items have mean μ = 70 and σ = 10. Compared with P(one item > 73), the probability P(mean of 25 items > 73) is:
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2026
A population has mean μ = 64 and standard deviation σ = 12. Find the smallest sample size n for which the standard error of the sample mean is at most 1.5.
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