Problem:
The arcade photo booth at Bill and Ted's Excellent Adventure Center shoots and processes silly photos in exactly 90 seconds (constant). Customers arrive at the booth according to a Poisson distribution at the mean rate of 30 per hour. On the basis of this information, determine the following:
a. the average number of customers waiting to use the photo booth
b. the average time a customer spends in the system
c. the probability an arriving customer must wait for their turn.