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# Confidence Interval III

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A chain of launderettes is investigating the lifetime of the washing machines that they use, measured in the number of washes completed before they need repairing. There are a number of machines used throughout their branches that have been installed at different times with each one having the number of completed washes recorded. To sample the lifetime of the washing machines the most recent 125 machines that have failed had their lifetimes recorded. This sample had a mean lifetime of 3124 hours and a variance of 2017.

a) Calculate a 95% confidence interval for the average lifetime of the washing machines that the company uses.

b) Calculate the sample size required to reduce the margin of error for a 95% confidence interval down to 7 (i.e. E = 7).

Please do not use excel functions. I would like to see clear workings and commentary for calculations.