Answer: (1.55, 6.45)
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 : Significance level : [tex]\alpha: 1-0.99=0.01[/tex]
Critical value : [tex]z_{\alpha/2}=2.576[/tex]
Sample size : n=41
Sample mean : [tex]\overline{x}=4.0\text{ kg}[/tex]
Standard deviation : [tex]\sigma=6.1\text{ kg}[/tex]
Then, 99% confidence interval for population mean will be :_
[tex]4\pm\ (2.576)\dfrac{6.1}{\sqrt{41}}\\\\\approx4\pm2.45\\\\=(4-2.45, 4+2.45)=(1.55, 6.45)[/tex]
