Answer: (2823, 3417)
Explanation:
The confidence interval for the population mean is given by :-
[tex]\mu\ \pm E[/tex], where E is the margin of error.
Formula for Margin of error :-
[tex]z_{\alpha/2}\times\dfrac{\sigma}{\sqrt{n}}[/tex]
Given : Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Sample size = 20
[tex]\mu=3120[/tex]
[tex]\sigma=677[/tex]
Critical value : [tex]z_{\alpha/2}=z_{0.025}=\pm1.96[/tex]
Margin of error : [tex]E=1.96\times\dfrac{677}{\sqrt{20}}\approx 297[/tex]
Now, the 95% confidence interval for the population mean will be :-
[tex]3120\ \pm\ 297 =(3120-297\ ,\ 3120+297)=(2823,\ 3417)[/tex]
