Sampling distribution of a proportion

Math

Definition

The probability distribution of all possible sample proportions from samples of a fixed size drawn from a population. It is approximately normal when np ≥ 10 and n(1−p) ≥ 10, centered at the population proportion p.

Examples

  • Repeatedly polling 200 voters and recording the proportion who support a candidate each time
  • Sampling 100 manufactured parts and recording the proportion that are defective across many samples
Key Fact

Standard error = √(p(1−p)/n)

Related Terms

Central limit theorem Confidence intervals for proportions Hypothesis tests for proportions Sampling methods

Study This Concept

Practice sampling distribution of a proportion with free review games in these units:

AP Statistics Unit 5: Sampling Distributions