5) (1 point) Triathlon times. In triathlons, itis 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 whileMary competed in the Women, Ages 25 - 29 group. Leocompleted the race in 4534 seconds, while Mary completed the racein 5534 seconds. Obviously Leo finished faster, but they arecurious about how they did within their respective groups. Can youhelp 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 hasa mean of 4315 seconds with a standard deviation of 599seconds.

The finishing times of the Women, Ages 25 - 29 grouphas a mean of 5274 seconds with a standard deviation of 786seconds.

The distributions of finishing times for both groups areapproximately Normal.

Remember: a better performance corresponds to a fasterfinish.

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 inhis group?  %.

6. What percent of the triathletes did Mary finish faster thanin her group?  %.

7. What is the cutoff time for the fastest 16% of athletes inthe men's group, i.e. those who took the shortest 16% of time tofinish?

seconds

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

seconds