You wish to estimate the mean winning time for Boston Marathon Women’s Open Division champions. The estimate must be within 0.13 hour of the population mean. Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Use the population standard deviation from Exercise 1.

Data from Exercises 1

The winning times (in hours) for a sample of 30 randomly selected Boston Marathon Women’s Open Division champions are shown in the table at the left.

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Women's Open Division winning times (in hours) 3.36 3.45 3.50 3.14 2.79 2.79 2.75 2.59 2.45 2.38 2.57 2.42 2.41 2.42 2.41 2.42 2.45 2.44 2.39 2.44 2.40 2.35 2.41 2.39 2.49 2.42 2.54 2.44 2.44 2.49