Problem Value: 1 point(s). Problem Score: 55%. Attempts Remaining: Unlimited. (1 point) Triathlon times. In triathlons,

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Problem Value 1 Point S Problem Score 55 Attempts Remaining Unlimited 1 Point Triathlon Times In Triathlons 1 (73.88 KiB) Viewed 93 times

Problem Value: 1 point(s). Problem Score: 55%. Attempts Remaining: Unlimited. (1 point) Triathlon times. 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 4892 seconds, while Mary completed the race in 5793 seconds. Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them? Round all calculated answers to four decimal places. Here is some information on the performance of their groups: The finishing times of the Men, Ages 30-34 group has a mean of 4309 seconds with a standard deviation of 577 seconds. The finishing times of the Women, Ages 25 - 29 group has a mean of 5257 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. 1. Write the short-hand for these two normal distributions The Men. Ages 30-34 group has a distribution of N 4309 577 The Women, Ages 25-29 group has a distribution of N 5257 807 2. What is the Z score for Leo's finishing time? z = 1.0104 3. What is the Z score for Mary's finishing time? z = 0.6642 4. Did Leo or Mary rank better in their respective groups? A. Leo ranked better B. They ranked the same C. Mary ranked better 5. What percent of the triathletes did Leo finish slower than in his group? % 6. What percent of the triathletes did Mary finish faster than in her group? % 7. What is the cutoff time for the fastest 20% of athletes in the men's group, i.e. those who took the shortest 20% of time to finish? seconds 8. What is the cutoff time for the slowest 34% of athletes in the women's group? seconds