Answer:
True cost of the microwave is in 99% confidence interval: [tex]c. $323.40 to $426.60[/tex]
Explanation:
Relevant data:
[tex]n=50\\\mu=375\\\sigma=20\\\alpha=0,001[/tex]
As we want to know the 99% confidence interval, the significance level is:
[tex](1-\alpha).100\%=99\%\\1-\alpha=0.99\\\alpha=0.01[/tex]
We need to estimate a confidence interval by a two tailed normal bell. Then we have:
[tex]Z_{\alpha/2}=Z_{0.005}[/tex]
The z-value for a probability of 0.005 in a normal standard distribution is 2.576
Confidence interval is given by;:
[tex]\=x\±Z_{\alpha/2}\sigma\\375\±Z_{\0.005}(20)\\375\±(2.58)(20)\\375\±51.60[/tex]
[tex]375+51.60=426.60\\375-51.60=323.40[/tex]
True cost of the microwave is in 99% confidence interval: [tex]c. $323.40 to $426.60[/tex]
