Answer
The sampling distribution of a statistic is a probability distribution for all possible values of the statistic, computed from a sample of size n with or without replacement.
Work Step by Step
In order to get a sampling distribution of the sample mean, one can follow the following steps:
Step-1: Obtain the random sample.
Step-2: Calculate the average of sample.
Step-3: Compare the sample mean with the population mean and repeat Steps 1 and 2 until all different simple indiscriminate samples of size n have been found.
In a simple indiscriminate sample of size n drawn from a population with average \[\mu \]and standard deviation \[\sigma \]
The sampling distribution of \[\bar{x}\] has average \[{{\mu }_{{\bar{x}}}}=\mu \]and standard deviation \[{{\sigma }_{{\bar{x}}}}=\frac{\sigma }{\sqrt{n}}\].
