3. 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 h 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) Write down the short-hand for these two normal distributions. b) What are the Z-scores for Leo's and Mary's finishing times? What do these Z-scores tell you? c) Did Leo or Mary rank better in their respective groups? Explain your reasoning. d) What percent of the triathletes did Leo finish faster than in his group? e) What percent of the triathletes did Mary finish faster than in her group?
3. 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 h 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) Write down the short-hand for these two normal distributions. b) What are the Z-scores for Leo's and Mary's finishing times? What do these Z-scores tell you? c) Did Leo or Mary rank better in their respective groups? Explain your reasoning. d) What percent of the triathletes did Leo finish faster than in his group? e) What percent of the triathletes did Mary finish faster than in her group?
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterP: Prologue: Calculator Arithmetic
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Transcribed Image Text:3. 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 hasa 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) Write down the short-hand for these two normal distributions.
b) What are the Z-scores for Leo's and Mary's finishing times? What do these Z-scores
tell you?
c) Did Leo or Mary rank better in their respective groups? Explain your reasoning.
d) What percent of the triathletes did Leo finish faster than in his group?
e) What percent of the triathletes did Mary finish faster than in her group?
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