David and Regina are competitive racers, and they both aim to break 2 minutes in their races. They are trying to figure out which who has the more difficult challenge, since they compete in different sports. David runs the 800-meter race and Regina swims the 200-meter freestyle. They agree to accept the following standards for high school boys and girls: boys’ 800-meter mean time is 149 seconds with a standard deviation of 13.6 seconds, girls’ 200-meter freestyle mean time is 145 seconds with a standard deviation of 8.2 seconds.
Currently, David’s best time is 2:02 minutes and Regina’s best time is 2:10 minutes. Assuming times in their respective events are normally distributed, find the percentile in which each David and Regina fall. Which athlete is relatively faster for their sport? Homework Help ✎
For David, calculate normcdf(122, 10^99, 149, 13.6).