Answer: [tex](182.356,\ 197.644)[/tex]
Step-by-step explanation:
Given : Significance level : [tex]\alpha:1-0.95=0.05[/tex]
Sample size : n=85
Critical value : [tex]z_{\alpha/2}=1.96[/tex]
Sample mean : [tex]\overline{x}=190[/tex]
Standard deviation : [tex]\sigma=11.7[/tex]
The confidence interval for population mean is given by :-
[tex]\overline{x}\pm z_{\alpha/2}\dfrac{\sigma}{\sqrt{n}}\\\\=190\pm(1.96)\dfrac{11.7}{\sqrt{9}}\\\\=190\pm7.644\\\\=(190-7.644,\ 190+7.644)=(182.356,\ 197.644)[/tex]
Thus, the 95% confidence interval for the true mean cholesterol content, μ, of all such eggs = [tex](182.356,\ 197.644)[/tex]
Hence, we conclude that the true population mean of amount of cholesterol lies between 182.356 and 197.644.
