### Home > INT3 > Chapter 5 > Lesson 5.1.3 > Problem5-49

5-49.

David and Regina are competitive racers, and they both aim to break two minutes in their respective races. They are trying to figure out 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, what is the percentile in which David and Regina each fall? Which athlete is relatively faster in his or her sport?

For David, calculate normalcdf$(122, 10^\wedge 99, 149, 13.6)$.