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 $93$ seconds completing his or her transactions. Transaction time is exponentially distributed.

a$.$ Determine the average time customers spend at the machine, including waiting in line and completing transactions. $($Do not round intermediate calculations. Round your answer to the nearest whole number.$)$

Average time minutes

b$.$ Determine the probability that a customer will not have to wait upon arriving at the automatic teller machine. $($Round your answer to $2$ decimal places.$)$

Probability

c$.$ Determine the average number of customers waiting to use the machine. $($Round your answer to $2$ decimal places.$)$

Average number

customers