In a certain very large city, the Department of Transportation (D. O.T.) has organized a complex system of bus transportation. In an advertising campaign, citizens are encouraged to use the new "GO-D. O.T!" system and head for the nearest bus stop to be transported to and from the central city. Suppose that at one of the bus stops the amount of time (in minutes) that a commuter must wait for a bus is a uniformly distributed random variable, T.
The possible values of T run from 0 minutes to 20 minutes.
(a) What is the probability that a randomly selected commuter will spend more than 7 minutes waiting for GO-D. O.T?
(b) What is the standard deviation?
(c) What is the probability that a randomly selected commuter will spend longer than 10 minutes but no more than 17 minutes waiting for the GO-D. O.T?
(d) What is the average waiting time?