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A local pizza parlor advertises that their average time for delivery of a pizza is within 30 minutes of receipt of the order. To check the accuracy of their claim, the delivery time for a random sample of 64 orders were recorded, with a sample mean of 34 minutes and a standard deviation of 21 minutes.

(i) Find a 99% confidence interval for the mean delivery time i.e. the population mean.

(iii) Find the sample size necessary to reduce the width of the confidence interval in (i) by half


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