The arrival time of my usual morning bus (b) is normally distributed, with a mean eta at 8: 00 am, and a standard deviation of 4 minutes. my arrival time (a) at the bus stop is also normally distributed, with a mean eta at 7: 50 am, and a standard deviation of 3 minutes. (a) with what probability can i expect to catch the bus? (hint: what is the distribution of the random variable x = a – b, and what must be true about x in the event that i catch the bus? ) (b) on average, how much earlier should i arrive, if i expect to catch the bus with 99% probability?