3.4 In triathlons, it is common for racers to be placed into age and g

3.4 In triathlons, it is common for racers to be placed into age and g

3.4 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 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo nished faster, but they are curious about how they did within their respective groups. Can you help them? Here is some information on the performanceof 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.In Exercise 3.4 we saw two distributions for triathlon times: N(4313; 583) for Men, Ages 30 – 34 and N(5261; 807) for the Women, Ages 25- 29 group. Times are listed in seconds.a) the cutoff time for the fastest 5% of athletes in the men’s group, i.e. those who took the shortest 5% of time to finishb) the cutoff time for the slowest 10% of athletes in the women’s group