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 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) What is the Z score for Leo's finishing time? (Round to the nearest hundredth.) b) What is the Z score for Mary's finishing time? (Round to the nearest hundredth.) c) Did Leo or Mary rank better in their respective groups? Select an answer Explain your reasoning.

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10:07 PM Mon Feb 8
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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.
Remember: a better performance corresponds to a faster finish.
a) What is the Z score for Leo's finishing time?
(Round to the nearest hundredth.)
b) What is the Z score for Mary's finishing time?
(Round to the nearest hundredth.)
c) Did Leo or Mary rank better in their respective groups? | Select an answer
Explain your reasoning.
d) What percent of the triathletes did Leo finish faster than in his group?
% (Round to the nearest
tenth of a percent.)
e) What percent of the triathletes did Mary finish faster than in her group?
% (Round to the nearest
tenth of a percent.)
f) If the distributions of finishing times are not nearly normal, would your answers to parts (d) and (e) change?
Explain your reasoning.
Submit Question
Transcribed Image Text:10:07 PM Mon Feb 8 O 37% A wamap.org 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. Remember: a better performance corresponds to a faster finish. a) What is the Z score for Leo's finishing time? (Round to the nearest hundredth.) b) What is the Z score for Mary's finishing time? (Round to the nearest hundredth.) c) Did Leo or Mary rank better in their respective groups? | Select an answer Explain your reasoning. d) What percent of the triathletes did Leo finish faster than in his group? % (Round to the nearest tenth of a percent.) e) What percent of the triathletes did Mary finish faster than in her group? % (Round to the nearest tenth of a percent.) f) If the distributions of finishing times are not nearly normal, would your answers to parts (d) and (e) change? Explain your reasoning. Submit Question
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