Southwest Arizona State University provides bus service to students while they are on campus. A bus arrives at the North Main Street and College Drive stop every 30 minutes between 6 A.M. and 11 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. What are the values for a and b? 

b. What is the mean of this uniform distribution? What is the standard deviation? 

c. Show that the total area is 1.0. 

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?