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 ​______.

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 .