Sampling distributions and the central limit theorem

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Useful for: AP® Statistics IB Math AI HL

Learn it Sample means x̄ from samples of size n have mean μ and standard deviation σ/√n. Sample proportions p̂ have mean p and SD √(p(1 − p)/n). For large n (about 30+), the sampling distribution of x̄ is approximately normal (central limit theorem).

Example: Bags of chips: μ = 250 g, σ = 8 g. SD of the mean of 16 bags?

σ/√n = 8/4.
= 2 g.

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