Question

1 point) In a recent collegiate men's 5000 meter speed skating competition, the average time was 401.9 seconds and the SD was 10.7 seconds. Assume that the times follow the normal curve and round all calculated results to four decimal places.

1. Find the percentage of skaters who would take longer than 435 seconds to finish the race. _________%

2. Using the normal curve, find a skater's time if he has a percentile rank of 69 (i.e. 31% of the skaters take longer than him to finish the race). ___________ seconds

Answer 1

Given that: u = 401.9 and o = 10.7 1) Calculate the percentage of skaters who would take longer than 435 seconds to finishthe race. P(X 435) 1-P(X 435) =1-P X-u 435-401.9" 10.7 -1-P(Z 3.09) (Use MS Excel -1-(NORMSDIST(3.09)) =1-0.998999 =0.001001 0.10% Hence, the required percentage is 0.10% 2) Calculate the time if he has percentile rank 69

P(Z <x) 69% PZ< =0.69 x-401.9(NORMSINV(0.69)) _ (Use Excel function) PZ < 10.7 x-401.9 = 0.49585 - 10.7 x-401.9 5.305599 401.953 05 599 x x 407.2056 = x 407.21 (Roumd to 2 decimal place) Hence, the required answer is: 407.21 seconds