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Sampling Distributions for Sample Proportions

AP Statistics· difficulty 3/5

A poll samples 1,000 of 200,000 voters; the true proportion supporting a candidate is p = 0.55.

p̂ ~ N(0.55, 0.0157)

Which sampling distribution best describes p̂?

  • A

    Skewed right with mean 0.55 and SD 0.55.

  • B

    Approximately normal with mean 0.55 and SD ≈ 0.0157.

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  • C

    Exactly normal with mean 0.55 and SD 0.5.

  • D

    Uniform on [0,1].

Explanation

Conditions met. σ_p̂ = √(0.55·0.45/1000) ≈ 0.0157.

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