Question

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 1:22:28 (4948 seconds), while Mary completed the race in 1:31:53 (5513 seconds). Obviously Leo finished faster, but they are curious about how they did within their respective groups. Can you help them?

Here is some information on the performance of their groups:

• The finishing times of the Men, Ages 30 - 34 group has a mean of 4313 seconds with a standard deviation of 583 seconds.

• The finishing times of the Women, Ages 25 - 29 group has a mean of 5261 seconds with a standard deviation of 807 seconds.

• The distributions of finishing times for both groups are approximately Normal.

Remember: a better performance corresponds to a faster finish.

(a) What percent of the triathletes did Leo finish faster than in his group?

(b) What percent of the triathletes did Mary finish faster than in her group?

(c) The fastest 5% of athletes in the men’s group get a medal, i.e. those who take the shortest 5% of time to finish. What is the cut off time to qualify for a medal?

(d) What is the cut off time for the slowest 10% of athletes in the women’s group.

Answer 1

a)

z score =(X-mean)/standard deviation=1.0892

Corresponding percentile score (faster)=

100-86.1966=13.8034 percentile

b)

z score =(X-mean)/standard deviation=0.3123

corresponding percentile score (faster)=

37.7419

c)

5 th percentile =mean+z*std deviation=4313+1.645*583 =

3354.0503

d)for slowest 10% will be at 90th percentile:

90th percentile =mean+z*standard deviation=

6295.2121