Question

Let x stand for the number of calories in each individual snack. 25 snacks are sampled at a time. The population mean is 95 calories and the population standard deviation is 2.5 calories What is the mean and standard deviation of the sampling distribution of sample means?

Answer 1

The mean of the sampling distribution of sample mean is the population mean itself.

The standard deviation of distribution of sample mean is given by,

$\sigma = \frac{\sigma}{\sqrt{n}}$

Hence,

$\bar{X}\rightarrow Norm(\mu, \frac{\sigma}{\sqrt{n}})$

We have n = 25.

$\frac{\sigma}{\sqrt{n}} = 2.5/\sqrt{25}=.5$

Mean of the sampling distribution of sample mean is 95 and

standard deviation of distribution of sample mean is 0.5