Question

Suppose a simple random sample of size n is drawn from a large population with mean and standard deviation. The sampling distribution of has mean ​______ and standard deviation ​______.

Answer 1

The sampling distribution of x has a mean μₓ = μ and standard deviation σₓ =​ σ/√n .

In the question, we are given that a random sample of size n is drawn from a large population with mean μ and standard deviation σ.

We are asked to find the mean and the standard deviation for the sampling distribution of the variable x for this sample.

The sample mean is regularly distributed, with a mean μₓ = μ and standard deviation σₓ = σ/√n, where n is the sample size, for samples of any size taken from populations that have a normal distribution.

Thus, the sampling distribution of x has a mean μₓ= μ and standard deviation σₓ=​ σ/√n .

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The provided question is incomplete. The complete question is:

"Fill in the blanks to correctly complete the sentence below.

Suppose a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ.

The sampling distribution of x has mean μₓ =​______ and standard deviation σₓ =​______."