Problem: Usually Meixiu drives to school and the driving time is between 10 to 20 minutes, depending on how manyred lights she encounters on the way. There are two traffic lights on her way to school. If she encounters nored lights, the driving time is anywhere between 10 and 15 minutes. If she is stopped by only one red trafficlight, it takes her anywhere between 13 and 18 minutes. If she hits two red lights, it takes anywhere between17 and 20 minutes to get to school. Assume it is equally likely for Meixiu to encounter no red lights, one redlight and two red lights.

Required:

a) What is the probability the Meixiu spent less than 15 minutes to drive to school today?

b) On Monday, Meixiu was not stopped by any red lights on her drive to school. What is the probabilitythat her drive was between 12 and 14.5 minutes on Monday?

c) What is the standard deviation of Meixiu's driving time on a day in which she encounters two red lights?

d) Knowing it took Meixiu less than 18 minutes to come to school, what is the probability that sheencountered only one red light?