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 4913 seconds, while Mary completed the race in 5705 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 4302 seconds with a standard deviation of 587 seconds.

The finishing times of the Women, Ages 25 - 29 group has a mean of 5221 seconds with a standard deviation of 819 seconds.

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

Remember: a better performance corresponds to a faster finish.

What percent of the triathletes did Leo finish slower than in his group?

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

Answer 1

For Leo

X= 4913 sec

Mean and S.D for MEN group is

Z score for Leo= X-mean/ S.D

= 4913-4302/587

Z= 1.0409

P (X<4913)=P (Z<1.04)

Use the standard normal table to conclude that:

P (Z<1.04)=0.8508

85.08% Percent of the triathletes did Leo finish slower than in his group

For Mary

X= 5705 seconds

Mean and S.D for MEN group is

Z score for Leo= X-mean/ S.D

= 5705-5221/819

Z= 0.5910

=> P ( X>5705 )=P ( Z>0.59 )

Use the standard normal table to conclude that:

P (Z>0.59)=0.2776

27.76% percent of the triathletes did Mary finish faster than in her group.