2. [-/16 Points] DETAILS DIEZSTAT4 4.1.004. MY NOTES ASK YOUR TEACHER In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo and Mary both completed the Hermosa Beach Triathlon, where Leo competed in the Men, Ages 30-34 group while Mary competed in the Women, Ages 25-29 group. Leo completed the race in 1:23:23 (5003 seconds), while Mary completed the race in 1:31:51 (5511 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 performance of their groups. The finishing times of the Men, Ages 30-34 group has a mean of 4313 seconds with a standard deviation of 583 seconds. . The finishing times of the Women, Ages 25-29 group has a mean of 5261 seconds with a standard deviation of 807 seconds. . The distributions of finishing times for both groups are approximately Normal. Remember: a better performance corresponds to a faster finish. (a) Write down the short-hand for these two normal distributions. Men, Ages 30-34 NH = Women, Ages 25-29 NH = 6 = (b) What are the Z-scores for Leo's and Mary's finishing times? (Round your answers to two decimal places.) Z Leo = Z Mary What do these Z-scores tell you? Leo finished standard deviations ---Select--- |the mean of his group's finishing time and Mary finished standard deviations ---Select--- V|the mean of her group's finishing time. (c) Did Leo or Mary rank better in their respective groups? Explain your reasoning. Since a lower Z score indicates a ---Select--- V|finishing time, ---Select--- V|did better. (d) What percent of the triathletes did Leo finish faster than in his group? (Round your answer to two decimal places.) % (e) What percent of the triathletes did Mary finish faster than in her group? (Round your answer to two decimal places.) % (f) If the distributions of finishing times are not nearly normal, would your answers to parts (b)-(e) change? Explain your reasoning. The answer to part (b) ---Select--- V|change, since Z scores ---Select-- V| be calculated for distributions that are not normal. The answers to parts (c)-(d) ---Select--- V|change, since we ---Select--- V|use the Z table to calculate probabilities and percentiles without a normal model. You may need to use the appropriate table in the Appendix of Tables to answer this