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Statistics · AP · Sampling Distributions

CED focus

The Central Limit Theorem

This topic is assessed on the AP Exam.

Multiple-choice tips

  • Ask whether the limit is one-sided, two-sided, or DNE before computing.
  • Separate parameter vs statistic in the stem.
  • Eliminate choices that confuse sample data with sampling distribution.
  • Check Normal/Large Counts conditions on MC.
  • Recognize when CLT applies to means or proportions.

Free-response tips

  • Use ‘approaches’ language; cite IVT or continuity when justifying.
  • Name the parameter being estimated or tested.
  • State independence and sample size conditions.
  • Describe center, spread, and shape of a sampling distribution.
  • Connect sample size to standard error in words.

Common traps

  • Equating lim f(x) as x→a with f(a) when a hole exists
  • Confusing p with p̂ or μ with x̄
  • Using Normal model without checking conditions
  • Treating one sample histogram as the sampling distribution

Quick checklist

  • [ ] Can distinguish parameter and statistic
  • [ ] Can state conditions for a Normal model
  • [ ] Can describe how sample size affects variability

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