Question

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 4534 seconds, while Mary completed the race in 5534 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 4315 seconds with a standard deviation of 599 seconds.

The finishing times of the Women, Ages 25 - 29 group has a mean of 5274 seconds with a standard deviation of 786 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. Mary ranked better
B. Leo ranked better
C. They ranked the same

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 16% of athletes in the men's group, i.e. those who took the shortest 16% of time to finish?

seconds

8. What is the cutoff time for the slowest 31% of athletes in the women's group?

seconds

(PLEASE ANSWER THE WHOLE QUESTION)

(PLEASE BE VERY CAREFUL ON ROUNDING)

Answer 1

1:

The Men, Ages 30 - 34 group has a distribution of N(4315 , 599).

The Women, Ages 25 - 29 group has a distribution of N(5274 , 786).

2:

3:

4:

A. Mary ranked better

5:

Men that have finishing time greater than Leo's finishing time will complete the race slower than Leo.

Answer: 64.43%

6:

Women that have finishing time greater than Marry's finishing time will complete the race slower than Marry.

Answer: 37.07%

7:

Answer: 3722 seconds

8:

Answer: 5664 seconds