Repeat parts (b)-(e) of Exercise 7.17 for samples of size 1.

Consider the given question,

The samples of size 1 and the corresponding means is given below,

Here, Bill Gates is represented by G, Warren Buffett is represented by B, Larry Ellison is represented by E, Charles Koch is represented by C, David Koch is represented by D and Chris Walton is represented by W.

On constructing the dot plot for the sampling distribution of the sample mean,

The population mean wealth for six people is 46.5 billion.

Consider the table in part (b), it is clear that none of the sample means is equal to the population mean. Also, number of samples size 2 is 15.

$$\begin{gathered} P\left(\overline{x}=\mu \right)=\frac{0}{6} \\ =0 \end{gathered}$$

We need to find the $P\left(\mu -3\le \overline{x}\le \mu +3\right)$.

From the table obtained in part (b), it is clear that there are none sample means is equal to the population mean.

role="math" localid="1652612575626" $$\begin{gathered} P\left(\mu -3\le \overline{x}\le \mu +3\right)\mathit{=}P\mathit{(}\mathit{46}\mathit{.}\mathit{5}\mathit{-}\mathit{3}\mathit{\le }\overline{x}\mathit{\le }\mathit{46}\mathit{.}\mathit{5}\mathit{+}\mathit{3}\mathit{)} \\ =P\mathit{(}\mathit{43}\mathit{.}\mathit{\le }\overline{x}\mathit{\le }\mathit{49}\mathit{.}\mathit{5}\mathit{)} \\ =\frac{0}{15} \\ =0 \end{gathered}$$

On interpreting, we can say that there is $0\%$ change that the mean wealth of one person will be within 3billion of the population mean.