Question

If a population is distributed with a mean μ and a standard deviation σ, then the...

If a population is distributed with a mean μ and a standard deviation σ, then the distribution of sample means is distributed

A) normally with mean μ and standard deviation σ.

B) normally with mean μ and standard deviation σ/√(n).

C) with mean μ and standard deviation σ.

D) with mean μ and standard deviation σ/√(n).

Math   Statistics-And-Probability   
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Answer #1

If a population is distributed with a mean μ and a standard deviation σ, then the distribution of sample means is distributed

ans-> D) with mean μ and standard deviation σ/√(n).

Let denotes the sample mean for a sample of size n.

Now,

Mean of sample means =

and Variance of sample means =

and standard deviation of sample means =

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