Chapter 10.2, Problem 10.33E

To determine

To construct: a similar picture that shows the idea of the sampling distribution of a sample mean.

Explanation of Solution

Graph:

  

The sampling distribution of the sample mean is about normal when the sample is enough large (due to the central limit theorem; sample is assumed to be enough large sample size $n$ is at least 30).

The mean of the sampling distribution of the sample mean is equal to the population mean $\mu$ . ${\mu }_{\overline{x}}=\mu$

The standard deviation of the sampling distribution of the sample mean is the population standard deviation $\sigma$ divided by the square root of the sample size.

  ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}$

Thus the sampling distribution of the sample mean is about normal with mean $\mu$ and standard deviation $\frac{\sigma }{\sqrt{n}}$