### Home > CCA2 > Chapter Ch10 > Lesson 10.1.2 > Problem10-41

10-41.

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?

For David, calculate normcdf$(122, 10$^$99, 149, 13.6)$.