Please show all work and explanation to Receive FULL CREDIT

Please show all work and explanation to Receive FULL CREDIT!!!

Airport shuttles arrive at the pick-up location randomly between 5 and 15 minutes apart, and run continuously. What distribution describes this behavior? Assuming you arrive at an arbitrary time, what is the probability of waiting 5 minutes?

Solution

This is uniform distribution with a = 5 and b = 15

P(waiting 5 minutes) = P(10) = (10-5)/(15-5) = 5/10 = 0.5