Question 730068
I'll do the first part to get you started


a)

I'm assuming you want the 99% confidence interval of the population mean. Let me know if it's some other variable.


The sample mean is 23.3


The margin of error is


E = z*sigma/sqrt(n)


E = 2.576*sigma/sqrt(n) ... use a calculator to find the critical value for z (let me know if you need me to show you how to do this on a calculator)


E = 2.576*2/sqrt(50) ... plug in the other given values


E = 0.72860282733461


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The lower bound of the confidence interval is 


L = xbar - E


L = 23.3 - 0.72860282733461


L = 22.5713971726653



The upper bound of the confidence interval is 


L = xbar + E


L = 23.3 + 0.72860282733461


L = 24.0286028273347


So the 99% confidence interval for the population mean is 


(L, U) = (22.5713971726653, 24.0286028273347)