Sampling Distributions for Sample Means

AP Statistics· difficulty 2/5

A simulation generates 10,000 sample means with size n = 25 from a population. The histogram has center near 50 and SD near 2.

10,000 simulated x̄ values center ≈ 50

Which is the most plausible inference about the population?

  • A

    μ ≈ 50 and σ ≈ 2.

  • B

    μ ≈ 25 and σ ≈ 50.

  • C

    μ ≈ 2 and σ ≈ 50.

  • D

    μ ≈ 50 and σ ≈ 10.

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Explanation

Center of x̄ distribution ≈ μ = 50; SD ≈ σ/√n → 2 ≈ σ/√25 → σ ≈ 10.

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