Sampling Distributions for Sample Means

AP Statistics· difficulty 2/5

A population is moderately skewed with μ = 80, σ = 15. A sample of n = 50 is selected.

Which describes the sampling distribution of x̄?

A
$Uniform.$
B
$Exactly normal with mean 80 and SD 15.$
C
$Approximately normal with mean 80 and SD \approx 2.12.$
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D
$Skewed with mean 80 and SD 15.$

Explanation

By CLT, x̄ is approximately normal. SD = 15/\sqrt50 \approx 2.12.

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