Answer:
Follows are the solution to this question:
Step-by-step explanation:
[tex]95 \% \[/tex] the confidence level for z:
[tex]\alpha = 1 - 95 \% \\\\[/tex]
[tex]= 1 - 0.95 \\\\ = 0.05[/tex]
[tex]\to \frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\\\to Z \ \frac{\alpha}{2} = Z_{0.025} = 1.96[/tex]
Calculating the Margin of error:
[tex]E = Z\ \frac{\alpha}{2} \times ( \frac{\sigma}{\sqrt{n}})[/tex]
[tex]= 1.96 \times ( \frac{5000}{\sqrt{\sqrt{100}}})\\\\= 980[/tex]
The population means estimate a 95 % confidence interval is:
[tex]\to \bar{x} \frac{+}{-} E\\\\ = \$ 90000 \frac{+}{-} 980[/tex]
