Answer :
Answer:
The 90% confidence interval estimate of the mean annual income of all company presidents is ($579,545, $590,580).
Step-by-step explanation:
The information provided is:
[tex]n=80\\\sigma=30,000\\\bar x=585062.50\\\text{Confidence level} = 90\%[/tex]
The critical value of z for 90% confidence level is, 1.645.
Compute the 90% confidence interval estimate of the mean annual income of all company presidents as follows:
[tex]CI=\bar x\pm z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\\\\=585062.50\pm 1.645\times\frac{30000}{\sqrt{80}}\\\\=585062.50\pm5517.50\\\\=(579545, 590580)[/tex]
Thus, the 90% confidence interval estimate of the mean annual income of all company presidents is ($579,545, $590,580).
This interval implies that there is 90% probability that the true mean annual income of all company presidents is within this interval.