Many of a bank's customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of $90$ seconds completing his or her transactions. Transaction time is exponentially distributed. Determine the following:

a$.$ The average time customers spend at the machine, including waiting in line and completing transactions

b$.$ The probability that a customer will not have to wait upon arriving at the automatic teller machine

c$.$ The average number waiting to use the machine