Question

A population has a mean 82 and a standard deviation 16 . Find the mean and standard deviation of a sampling distribution of sample means with sample size n=64 .

Answer 1

The mean is 82 and the standard deviation of the sampling distribution is 2

Finding the mean and standard deviation of the sampling distribution

from the question, we have the following parameters that can be used in our computation:

Mean = 82

Standard deviation = 16

Sample size = 64

The mean of the sampling distribution of sample means is equal to the population mean,

So, we have

Mean. μ = 82.

The standard deviation of the sampling distribution of sample means is equal to the population standard deviation divided by the square root of the sample size

So, we have

σ = 16/√64

σ = 2

Hence, the mean is 82 and the standard deviation of the sampling distribution is 2