UHV provides bus service from the main campus to the dormitory located at US 59 Business Street. A bus arrives at the entrance of UHV West Wing building bus stop every 30 minutes between 8 A.M and 7 P.M. during weekdays. Students arrive at the bus stop at random times. The time that a student waits is uniformly distributed from 0 to 30 minutes

a. Draw a graph of this distribution.

b. Show that the area of this uniform distribution is 1.00.

c. How long will a student "typically" wait for a bus? (i.e. mean waiting time). What is the standard deviation of the waiting time?

d. What is the probability a student will wait more than 25 minutes?

e. What is the probability a student will wait between 10 and 20 minutes?