In triathlons, it is common for racers to be placed into age andgender groups. Friends Leo and Mary both completed the HermosaBeach Triathlon, where Leo competed in the Men, Ages 30-34group while Mary competed in the Women, Ages 25-29 group.Leo completed the race in 1:22:28 (4948 seconds) , while Marycompleted the race in 1:31:53 (5513 seconds). Obviously Leofinished faster, but they are curious about how they did withintheir respective groups. Can you help them? Here is someinformation on the performance of their groups:

• The finishing times of the Men, Ages 30-34 group havea mean of 4313 seconds with a standard deviation of 583seconds.
• The finishing times of the Women, Ages 25-29 grouphave a mean of 5261 seconds with a standard deviation of 807seconds.
• The distributions of finishing times for both groups areapproximately Normal.

Remember, a better performance corresponds to a fasterfinish.

1. Find the Z-scores for Leo’s and Mary’s finishing times. Did Leoor Mary rank better in their respective groups? Explain yourreasoning?
   
   

2. What percent of the triathletes did Leo finish faster than inhis group?
   
   
   
3. What percent of the triathletes did Mary finish faster than inher age group?
   

4. What is the cutoff time for the fastest 5% of athletes in themen’s group?

5. What is the cutoff time for the slowest 10% of athletes in thewomen’s group?