(11 points) Triathlon times. In triathlons, it is common for racers to be placed

Question

(11 points) 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 4944 seconds, while Mary completed the race in 5579 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 two 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 4316 seconds with a standard deviation of 586 seconds. The finishing times of the Women, Ages 25 - 29 group has a mean of 5267 seconds with a standard deviation of 787 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? 3. What is the Z score for Mary's finishing time? 4. Did Leo or Mary rank better in their respective groups? seconds A. Mary ranked better B. They ranked the same C. Leo ranked better

Explanation / Answer

1)the men , ages 30-34 group has a distribution of N (4316 , 5862)

the women , ages 25-29 group has a distribution of N (5267 , 7872)

2)

Z score for Leo's finishing time =(4944-4316)/586=1.07

3)

Z score for Mary's finishing time =(5579-5267)/787=0.40

4)

option A ; Mary Ranked better

5)

P(Z<1.07)=85.77%

6)

P(Z>0.4)=34.46%

7)

for 19 th percent ; z=-0.88

corresponding time =4316-0.88*586=3800.32 seconds

8)

for slow 36% ; crtical z =0.36

corresponding time =5267+0.36*787=5550.32 seconds

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