. Triathlon times. Friends Leo and Mary both completed the Herrnosa Beach Triathlon. In this triathlon, racers were placed into age and gender groups where Leo competed in the Men. Ages 39 - 34 group while Mary competed in the Women, Ages 25- 29 group. Leo completed the race in 1:22:40 (4960 seconds}. while Mary completed the race in 1:31:15 {5475 seconds]. Obviously Leo finished faster. but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performanco of their groups: The nishing times of the Men. Ages 30 - 34 group has a mean of 4352 seconds with a standard deviation of 524 seconds. The finishing times of the Women. Ages 25 - 29 group has a mean of 5232 seconds with a standard deviation of 524 seconds. The distributions of finishing times for both groups are approximately Normal. Remember: a better performance corresponds to a faster finish. (a) What are the 2 scores for Leo's and Mary's finishing times? What do these 2 scores tell you? (b) Would you expect Leo or Mary to have ranked better in their respective groups? Explain your reasoning. (c) Approximate the percentage of triathletes that finished slower than Leo in his group. (d) Approximate the percentage of triathletes that nished slower than Mary in her group. (e) If the distributions of nishing times are not nearly normally distributed. which of your answers to parts [a] (d) would change? Explain your reasoning. (f) Approximate the cutoff time for the fastest 15% of athletes in the men's group. i.e. those who took the shortest 15% of time to finish. Give your answer to the nearest second. (g) Approximate the cutoff time for the slowest 10% of athletes in the women's group. Give your answer to the nearest second. [1] [2] [2] l2] [2] [2]