Answer: (1.4964, 1.5126)
Step-by-step explanation:
We know that the confidence interval for population mean is given by :-
[tex]\overline{x}\ \pm z*\dfrac{\sigma}{\sqrt{n}}[/tex]
, where [tex]{\sigma[/tex]= population standard deviation.
n= sample size
[tex]\overline{x}[/tex] = Sample mean
As per given , we have
σ = 0.01 inches
n= 10
[tex]\overline{x}=1.5045[/tex]
Also, the critical value for 99% confidence interval = [tex]z*=2.576[/tex] [From x-value table.]
[Significance level =1-0.99=0.01 and [tex]z_{\alpha/2}\ at\ \alpha=0.01[/tex] is 2.576.]
Then, the 99% two-sided confidence interval on the mean hole diameter will be :-
[tex]1.5045\ \pm (2.576)\dfrac{0.01}{\sqrt{10}}\\\\\approx1.5045\pm(2.576)(0.00316)=1.5045\pm0.00814016=(1.5045-0.00814016,\ 1.5045+0.00814016)\\\\=(1.49635984,\ 1.51264016)\approx(1.4964,\ 1.5126)[/tex]
Hence, the required confidence interval = (1.4964, 1.5126)
