4.4 Triathlon Times, Part I: 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 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.
a) How many standard deviations longer than average time did Leo take to finish the race within his gender and age grouping? That is, find his z-score.
(please round to two decimal places)
b) How many standard deviations longer than average time did Mary take to finish the race within her gender and age grouping? That is, find her z-score.
(please round to two decimal places)
c) Which of the runners placed relatively better within their respective groupings?
d) What runners in his group did Leo place better than?
% (please round to two decimal places)
e) What percentage of runners in Mary's group did she place better than?
% (please round to two decimal places)