A student takes the campus shuttle bus to reach the classroom building. The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. The student allows 10 minutes waiting time for the shuttle in his plan to make it in time to the class.
a. What is the expected waiting time? What is the variance?
b. What is the probability that the wait will be between four and six minutes?
c. What is the probability that the student will be in time for the class?
d. If he wants to be 95% confident of being on time for the class, how much time should he allow for waiting for the shuttle?