Answer: (24755, 25245)
Step-by-step explanation:
Given : Sample size : n= 400
Sample mean : [tex]\overline{x}= \$25,000[/tex]
Standard deviation : [tex]\sigma=\$2,500[/tex]
Significance level : [tex]\alpha: 1-0.95=0.05[/tex]
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm\ z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=25000\pm(1.96)\dfrac{2500}{\sqrt{400}}\\\\=25000\pm245\\\\=(25000-245,\ 25000+245)=(24755,\ 25245)[/tex]
Hence, the 95% confidence interval for the mean salary of all graduates from the English department is (24755, 25245)
