Chapter 7.3, Problem 54E

(a)

To determine

To find: the mean of the sampling distribution of $\overline{x}$ .

Answer to Problem 54E

40.125 mm

Explanation of Solution

Given:

  $\begin{array}{l}\mu =40.125\\ \sigma =0.002\\ n=4\end{array}$

Calculation:

The mean of the sampling distribution of the sample mean is equal

  ${\mu }_{\overline{x}}=\mu =40.125$

The units of the mean of the sampling distribution of the sample mean are the sample as the units of the population mean and thus the mean is $40.125$ mm

(b)

To determine

To Calculate: and interpret the standard deviation of the sampling distribution of $\overline{x}$ .

Answer to Problem 54E

0.001 mm

Explanation of Solution

Given:

  $\begin{array}{l}\mu =40.125\\ \sigma =0.002\\ n=4\end{array}$

Formula used:

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

Calculation:

The mean of the sampling distribution of the sample mean is

  ${\mu }_{\overline{x}}=\mu =40.125$

The standard deviation of the sampling distribution of the sample mean is

  ${\sigma }_{\overline{x}}=\frac{\sigma }{\sqrt{n}}=\frac{0.002}{\sqrt{4}}=\frac{0.002}{2}=0.001$

The units of the standard deviation of the sampling distribution of the sample mean are the same the units of the population standard deviation and therefore the standard deviation is $0.001\text{mm}$ .

The sample mean diameter of 4 randomly selected axles in an hour varies on average by $0.001$ mm from the mean diameter of $40.125$