Chapter 6.2, Problem 6CS

A marathon is a fool race with a distance of 26.22 miles. It was one of the original events of the modem Olympics, where it was a men’s only event. The women’s marathon became an Olympic event in 1984. The Olympic record for the men’s marathon was set during the 2008 Olympics by Samuel Kamau Wanjiru of Kenya, with a time of 2 hours, 6 minutes, 32 seconds. The Olympic record for the women’s marathon was set during the 2012 Olympics by Tiki Gelana of Ethiopa, with a time of 2 hours. 23 minutes, 7 seconds.

Training for a marathon typically lasts at least 6 months. The training is gradual, with increases in distance about every 2 weeks. About 1 to 3 weeks before the race, the distance run is decreased slightly. The stem-and-leaf plots below show the marathon training times (in minutes) for a random sample of 30 male runners and 30 female runners.

6. A trainer wants to estimate the population mean running times for both male and female runners within 2 minutes. Determine the minimum sample size required to construct a 99% confidence interval for the population mean training time of

1. (a) male runners. Assume the population standard deviation is 8.9 minutes.
2. (b) female runners. Assume the population standard deviation is 8.4 minutes.