In triathlons, it is common for racers to be placed into age and gender groups.

Question

In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Helena Triathlon, where Leo competed in the Men, Ages 30-34 group while Mary complete in the Women, Age 25 - 29 group. Leo completed the race in 1 hour, 23 minutes, and 13 seconds (a total of 4993 seconds), while Mary completed the race in 1 hour, 35 minutes, and 6 seconds (a total of 5706 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Here is some information on the performance of their groups. The finishing times of the Men, Ages 30 - 34 group has a mean of 4300 seconds with a standard deviation of 576 seconds The finishing times of the Women, Ages 25 -29 group has a mean of 5272 seconds with a standard deviation of 801 seconds. The distributions of finishing times for both groups are approximately normally distributed. (a) What is the z-score for Leo's time? 1.2031 (b) What is the z-score for Mary's time? 0.541822 (c) Did Leo or Mary rank better in their respective groups? (remember that faster times are better) A. Leo did better in his group. B. They ranked the same. OC. Mary did better in her group. For the next two questions remember that a person that went faster in the triathlon has a smaller time. (d) What percent of the triathletes did Leo finish faster than in his group? (e) What percent of the triathletes did Mary finish faster than in her group?

Explanation / Answer

d) P(Z >1.2) = 1 - P(Z < 1.2) = 1 - 0.8849 = 0.1151 = 11.51%

Leo finished 11.51% of the triathletes faster than in his group.

e) P(Z > 0.54) = 1 - P(Z < 0.54) = 1 - 0.7054 = 0.2946 = 29.46%

Marry finished 29.46% of the triathletes faster than in his group.

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