Question: Suppose the AC transit bus scheduled to arrive at my corner at 8:10 A. M. but its actual arrival time is normal random variable with mean 8:10 A.M. and standard deviation 40 seconds suppose I try to arrive at the corner at 8:09, but my arrival time is actually normally distributed with mean 8:09 A.M., and standard deviation 30 seconds.
a) What percentage of the time do I arrive at the corner before the bus is scheduled to arrive?
b) What percentage of the time do I arrive at the corner before the bus does?
c) If I arrive at the stop at 8:09 A.M. and the bus still hasn't come by 8:12 A.M what is the probability that I have already missed it?