It takes the bus an average of 20 minutes to arrive at a certain bus stop. A student is waiting for the next bus to arrive.
(a) What is the probability the student waits more than 30 minutes?
(b) What is the probability the student waits exactly 15 minutes?
(c) What is the probability the student waits more than 45 minutes (total) given they've already waited 20 minutes.
(d) Given the student waited less than 45 minutes, what is the probability they waited less than 20 minutes?
(e) What is the standard deviation of waiting time?