Question

s the statement below true or​ false? The distribution of the sample​ mean, x overbar​, will be normally distributed if the sample is obtained from a population that is normally​ distributed, regardless of the sample size.

Answer 1

True

Explanation:

Assume the following

Mean is represented by μ

Standard deviation by σ

Sample mean by x

Sample Size by n

Given that all possible values of a random variable calculated from a sample of size n with a population mean and standard deviation μ and σ, respectively, it's known that the sampling distribution of the sample mean x is its probability distribution.

Having said that, assume that a simple random sample of size n is drawn from a large population with mean μ and standard deviation σ, as stated above.

The sampling distribution of x will be distributed normally as long as the random variable is normally​ distributed.