Question

JUNIJ. De Uw ale nuights of 25 female college students. Stu al. Grades (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 4908 seconds, while Mary completed the race in 5591 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 4310 seconds with a standard deviation of 579 seconds. The finishing times of the Women, Ages 25 - 29 group has a mean of 5297 seconds with a standard deviation of 843 seconds. The distributions of finishing times for both groups are approximately Normal. Remember a better performance corresponds to a faster finish. 1. Write the short-hand for these two normal distributions. The Men, Ages 30-34 group has a distribution of NC The Women, Ages 25 - 29 group has a distribution of N 2. What is the Z score for Leo's finishing time? z = 3. What is the Z score for Mary's finishing time? z = 4. Did Leo or Mary rank better in their respective groups? A. Leo ranked better B. They ranked the same C. Mary ranked better 5. What percent of the triathletes did Leo finish slower than in his group?

Answer 1

Leo, Men (30-34 ag Men ( 30-34 age group) completed the race Tet x be the time in which leo completed such that in 4908 see. reace. X - 4908 Mean = 4310 = 4 Variante = (579)- 0-2 Sto deviation - 57975 for women (25-29 age group). let y be the time in which ie Y= 5591 Mean = 5297-u variance =(843)² = 02 ste, deulation 843=0 Marry completed race XNNIH, 62) NN (4310, (579²) NN (4310, 335241) YN N(4,02) NN(5591, (84334 ~ N(5591, 710649)

& -score for Leo's finising time. Z = X-M NN(0,1) Now for x=4908 M = 4310 T=579 Zx = 990 8 - [ 31 0 579 Zx = 1:03 z-score for Marry's finishing time- 2= x-h wN001) - 5591 - 5297 843 Zy = 0.39) (9 Rank of & Leo's is better than marry's Rank. because it depends on 2-score. Leo has greater 2-score then Marry's z-score. [Zx724) So, Leo's get better Rank.