Question

Define the sampling distribution of the mean

Answer 1

Sampling distribution of the mean :

Suppose simple random sample of size ' n ' is drawn from any population with mean and standard deviation then

according to Central Limit theorem for large n ( n > 30 ) the sampling distribution of sample mean ( ) is approximately normal with mean and standard deviation

Example : Let simple random sample of size 50 drawn form population with mean = 10 and standard deviation = 2.

Here n > 30 so according to central limit theorem distribution of sampling distribution of sample mean is normal with mean and standard deviation    

Note that if sample is drawn from normal population then it not necessary that n > 30