91Ó°ÊÓ

Let n denotes the number of vice presidents that is n=2193

The mean salary is $\stackrel{¯}{x}=\$116754$

The sample standard deviation is s = $ 39185

The population size is

The 95% confidence intervals for the population mean is as follows,

Consider,

$$\begin{gathered} \frac{n}{N}=\frac{223}{2193} \\ =0.1017 \end{gathered}$$

Here,$\frac{n}{N}=0.1017>0.05$the finite population correction factor should be included in the standard error calculation.

The 95% confidence intervals for the population mean by using the following formula,

$\stackrel{¯}{x}Â\pm 2\frac{s}{\sqrt{n}}\sqrt{\frac{N-n}{N}}$

Therefore

.$$\begin{gathered} \stackrel{¯}{x}Â\pm 2\frac{s}{\sqrt{n}}\sqrt{\frac{N-n}{N}}=116754Â\pm 2\left(\frac{39185}{\sqrt{223}}×\sqrt{\frac{2193-223}{2193}}\right) \\ =116754Â\pm 4974.06 \\ =\left(111779.9,121728.1\right) \end{gathered}$$

Hence, the required confidence interval is (111779.9, 121728.1).

The confidence interval for the mean salary of the vice presidents is (111779.9, 121728.1). Thus, it is 95% confident that the true mean salary of the vice presidents falls between $111779.9 and $121728.1.