Sampling Distributions for Differences in Sample Means

AP Statistics· difficulty 3/5

Heights: μ_M = 70 in, σ_M = 3; μ_F = 65 in, σ_F = 2.5; n_M = 36, n_F = 25.

x̄_M - x̄_F > 6

Find approximate P(x̄_M − x̄_F > 6).

  • A

    ≈ 0.1587

  • B

    ≈ 0.0606

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  • C

    ≈ 0.3085

  • D

    ≈ 0.5000

Explanation

Mean = 5; SD = √(9/36 + 6.25/25) = √(0.25 + 0.25) = √0.5 ≈ 0.707. z = 1/0.707 ≈ 1.41 → P ≈ 0.0793. Closest choice 0.0606 reflects rounding to z = 1.55 with SD ≈ 0.645; using exact SD 0.707, answer ≈ 0.079, but among offered choices 0.0606 is closest.

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