2012 NYJC P2 Q10

Every morning, Peter has to take a bus to school.On average, he reaches the bust stop at 6:30am each day.His arrival time at the bus stop is normally distributed with a standard deviation of 10 minutes.The first bus will leave the bust stop at 6:40am sharp and the second bus will leave at 6:50am sharp.Regardless of the time the busses leave the bus stop, the bus journey will follow a normal distribution with mean 45 minutes and standard deviation 20 minutes.Peter will be late if he arrives at school after 7:30 am or if he misses the 6:50 am bus.

Assuming that the time Peter reaches the bus stop and the time taken for the bus journey are independent, find the probability that

1. Peter will miss the 6:50 am bus.
2. Show the probability that Peter will be late for school is 0.442.