(1 point) Triathlon times. In triathlons, it is common for racers to be placed into age and gender groups. Friends Leo a

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(1 point) Triathlon times. 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 4530 seconds,
while Mary completed the race in 5704 seconds. Obviously Leo
finished faster, but they are curious about how they did within
their respective groups. Can you help them? Round all calculated
answers to four decimal places.
Here is some information on the performance of their groups:
The finishing times of the Men, Ages 30 -
34 group has a mean of 4306 seconds with a standard
deviation of 598 seconds.
The finishing times of the Women, Ages 25 -
29 group has a mean of 5236 seconds with a standard
deviation of 758 seconds.
The distributions of finishing times for both groups are
approximately Normal.
Remember: a better performance corresponds to a faster
finish.
1. Write the short-hand for these two normal distributions.
The Men, Ages 30 - 34 group has a
distribution of N( , ).
The Women, Ages 25 - 29 group has a
distribution of N( , ).
2. What is the Z score for Leo's finishing time? z =
3. What is the Z score for Mary's finishing time? z =
4. Did Leo or Mary rank better in their respective groups?

A. They ranked the same
B. Leo ranked better
C. Mary ranked better
5. What percent of the triathletes did Leo finish slower than in
his group? %.
6. What percent of the triathletes did Mary finish faster than
in her group? %.
7. What is the cutoff time for the fastest 10% of athletes in
the men's group, i.e. those who took the shortest 10% of time to
finish?
seconds
8. What is the cutoff time for the slowest 20% of athletes in
the women's group?
seconds