{11 pclnts}1'i'tathlon tines. 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 \"53 seconds. while Mary completed the race In 52'23 seconds. Obviously Leo nlshed faster, but they are curious about how they did within their respective groups. Can you help them? Ftcund all calculated answers to two decimal places. Here Is some infom'latlon on the performance of their groups: The finishing times of the Men. Ages 30 - 34 group has a mean of 43m seconds with a standard deviation of 592 seconds. The finishing times of the women. Ages 25 - 29 group has a mean of 525? seconds with a standard deviation of T85 seconds. The distributions of finishing times for both groups are approximately Non'nal. Fiernember: a better performance corresponds to a faster finish. 'I . Write the short-hand for these two normal distributions. The Men, Ages so - 34 group has a distribution of N1: , ]. The Iillit'rrrren, Ages 25 - 29 group has a distribution of NI: , i. 2. What is the 2 score for Leo's nishing time? 2 = 3. What is the 2 score for Mary's nishing time? 2 = 4. Did Leo or I'lllarglI rank better In their respective groups? (:1. A. Leo ranked better (:1. B. They.I ranked the same (:1. C. ltllaryr ranked better 5. What peroent of the triathletes did Leo 'finish slower than in his group? '96. 6. What peroent of the triathletes did ltllaryr 'finish faster than In her group? 916. i". What is the cutoff time for the fastest 12% of athletes in the men's group, Le. those who took the shortest 12% of time to finish? Exams 5. What is the cutoff time for the slowest 13% of athletes in the women's group? seconds