Pan usually drives to school. The driving time is between 10 to 20 minutes depending on how many red lights he encounters on the way. There are two traffic lights on his way to school. If he encounters no red lights, the driving time is anywhere between 10 to 15 minutes. If he is stopped by only one red traffic light, it takes him anywhere between 13 to 18 minutes. If he hits two red lights, it takes anywhere between 17 to 20 minutes to get to school. Assume it is equally likely for Pan to encounter no red lights, one red light and two red lights.
a) On Monday, Pan was not stopped by any red lights on his drive to school. What is the probability that his drive was between 12 and 14.5 minutes on Monday?
b) What is the standard deviation of Pan's driving time on a day in which he encounters two red lights?
c) What is the probability the Pan spent less than 15 minutes to drive to school today?
d) Knowing it took Pan less than 18 minutes to come to school, what is the probability that he encountered only one red light?