In current Austin marathon, the distribution of finishing times for the female runners who completed the race were approximately normally distributed with a mean of 280 minutes and a standard deviation of 49 minutes. For male runners who completed the race, their finishing times were normally distributed with a mean of 256 minutes and a standard deviation of 42 minutes. Also, 40% of the racers who finished were female.
You want to compare the proportion of males and females who finished the race under 4 hours. Draw a probability tree for this scenario.
What proportion of all racers who completed the marathon finished in under 4 hours?