(11 points) 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 4870 seconds, while Mary completed the race in 5504 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.

Missing items in question are:

- 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.

- Mary was only 0.31 SD’s above the mean for her group, and Leo was 1.09 SD’s above the mean for his group, thus Mary ranked better in her group than Leo did in

his group .

- Leo finished faster than 13.8% of the runners in his group.

-mary finished faster than 37.8% of the runners in her group.

Step-by-step explanation:

(A) Let M denote the finishing times for men, ages 30-34. Then, the normal distribution of finishing times is M ∼ N(4313, 583).

Now, let W denote the finishing times for women, ages 25-29. Then the normal distribution of finishing times is W ∼ N(5261, 807).

B) Leo’s z-score is; Z = (M - μm) / σm = (4948−4313) / 583 = 1.09

Mary’s z-score is Z = (W - μw) / σw = ( 5513−5261) / 807 = 0.31

From these 2 values of leo and mary, it means that Mary was 0.31 Standard deviations above the mean for her group, and Leo was 1.09 Standard deviations above the mean for his group.

C) From B above, we can deduce that; Since Mary was only 0.31 SD’s above the mean for her group, and Leo was 1.09 SD’s above the mean for his group, then Mary ranked better in her group than Leo did in

his group.

D) From 1-pnorm(c(1.09) in p-norm calculator, P(Z > 1.09) = 0.138; then Leo finished faster than 13.8% of the runners in his group.

E) Also from 1-pnorm(c(0.31) in p-norm calculator, P(Z > 0.31) = 0.378; them mary finished faster than 37.8% of the runners in her group.

F) This was solved with the assumption that the distributions of finishing times for both groups are approximately Normal

0.02

step-by-step explanation:

time of 9 192 631 770 periods of the radiation corresponding to the transition between the 2 hyperfine levels of the ground state of the caesium 133 atom at 0 k (but other seconds are sometimes used in astronomy)