Solution
Given the following below
[tex]\begin{gathered} \bar{x}=\text{ \$126}.00 \\ n=40 \\ \sigma=\text{ \$18.60} \\ At\text{ 90\% the critical z is }\pm1.645 \end{gathered}[/tex]
To find the 90% confidence interval, the formula is
[tex]\bar{x}\pm z\frac{\sigma}{\sqrt[]{n}}[/tex]
Substituting values into the formula above
[tex]126\pm1.645\frac{18.6}{\sqrt[]{40}}[/tex]
Solve the above
[tex]\begin{gathered} 126+_{}1.645\frac{18.6}{\sqrt[]{40}}=130.84\text{ (two decimal places)} \\ 126-1.645\frac{18.6}{\sqrt[]{40}}=121.16\text{ (two decimal place)} \end{gathered}[/tex]
At 90% confidence interval, the population mean will be between 121.16 and 130.84 (121.16, 130.84)
