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The Central Limit Theorem

AP Statistics· difficulty 3/5

Income in a region is strongly right-skewed with μ = 50,000andσ=50,000 and σ =25,000. A random sample of n = 64 incomes is selected.

Right-skewed population

Which statement best describes the sampling distribution of x̄?

  • A

    Right-skewed with mean 50,000andstandarddeviation50,000 and standard deviation25,000.

  • B

    Uniform with mean $50,000.

  • C

    Approximately normal with mean 50,000andstandarddeviation50,000 and standard deviation3,125.

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  • D

    Exactly normal with mean 50,000andstandarddeviation50,000 and standard deviation25,000.

Explanation

By the CLT (n = 64 ≥ 30), x̄ is approximately normal. Mean = μ = 50,000;σxˉ=25000/√64=50,000; σ_x̄ = 25000/√64 =3,125.

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