) In triathlons, it is common for racers to be placed into age and gender groups. Friends Romeo and Juliet both completed the Verona Triathlon, where Romeo competed in the Men, Ages 30-39 group while Juliet competed in the Women, Ages 20-29 group. Romeo completed the race in 4848 seconds, while Juliet completed the race in 5413 seconds. While Romeo finished faster, they are curious about how they did within their respective groups. Here is some information on the performance of their groups. The finishing times of the Men, Ages 30-39 group has a mean of 4213 seconds with a standard deviation of 583 seconds. The finishing times of the Women, Ages 20-29 group has a mean of 5061 seconds with a standard deviation of 807 seconds. The distributions of finishing times for both groups are approximately Nor- mal. Remember: a better performance corresponds to a faster finish. (a) Write the distribution for Men Ages 30-39 and the distribution for Women Ages 20-29 as normal distributions N(,), where is the mean and is the standard deviation. (b) What are the Z-scores for Romeo's and Juliet's finishing times? What do these Z-scores tell you? (c) Did Romeo or Juliet rank better in their respective groups? Explain your reasoning. (d) What percent of the triathletes were slower than Romeo in his group? (e) What percent of the triathletes were slower than Juliet in her group? (f) Compute the cutoff time for the fastest 5% of athletes in the men's group, i.e. those who took the shortest 5% of time to finish. (This is in the 5th percentile of the distribution). (g) Compute the cutoff time for the slowest 10% of athletes in the women's group. (This is in the 90th percentile of the distribution)