Metro buses are scheduled to arrive at each stop every 30 mi

Metro buses are scheduled to arrive at each stop every 30 minutes. If the time a person waits at a bus stop is uniformly distributed and the maximum possible wait time for a bus is 30 minutes, what is the probability that you will wait more than 25 minutes for a bus?

Solution

The minimum wait time is of course 0. Thus,          
a = lower fence of the distribution =    0      
b = upper fence of the distribution =    30      
          
          
Note that P(x>c) = P(c<x<b) = (b-c)/(b-a). Thus, as          
          
c = critical value =    25      
          
Then          
          
P(x<c) = (30-25)/(30-0) =   0.166666667   [ANSWER]