Sorry for the essay but its long .
Flooding has washed out one of the tracks of a railroad company. The railroad has two parallel tracks from baker to Cooper, but only on usable track from Cooper to Daniel, as shown below ( i drew it in the attachment ). Having only one usable track disrupts the usual schedule. Until it is repaired, the washed-out track will remain unusable. If the train leaving Baker arrives at Cooper first, it has to wait until the train leaving Daniel arrives at Cooper.
(look at picture)
Every day at noon a train leaves Baker heading for Daniel and another leaves Daniel heading for baker.
Assume that the length of time, X, it takes the train leaving Baker to get to Cooper is normally distributed with a mean of 170 minutes and a standard deviation of 20 minutes.
Assume that the length of time, Y, it takes the train leaving Daniel to get to Cooper is normally distributed with a mean of 200 minutes and a standard deviation of 10 minutes.
These two travel times are independent.
1.) What is the distribution of Y-X
2.) Over the long run, what proportion of the days will the train from Baker have to wait at Cooper for the train from Daniel to arrive?
3.) How long should the railroad company delay the departure of the train from Baker so that the probability that it has to wait is only 0.01?