Answer: [tex](24980.25,\ 25419.75)[/tex]
Step-by-step explanation:
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}[/tex]
Given : Sample size : [tex]n= 179 [/tex] , which is a large sample , so we apply z-test .
Sample mean : [tex]\overline{x}=20200+5000=25200 [/tex]
Standard deviation : [tex]\sigma= 1500[/tex]
Significance level : [tex]\alpha=1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Now, a confidence interval at the 95% level of confidence will be :-
[tex]25200\pm(1.96)\dfrac{1500}{\sqrt{179}}\\\\\approx25200\pm219.75\\\\=(25200-219.75,\ 25200+219.75)\\\\=(24980.25,\ 25419.75)[/tex]
