Award: $10\mathrm{.}00$ points

Many of a bank's customers use its automated banking machine $($ABM$).$ During the early evening

hours in the summer months, customers arrive at an ABM at the rate of one every other minute

$($assume Poisson$).$ Each customer spends an average of $99$ seconds completing the transaction.

Transaction times are exponentially distributed. Assume that the length of the queue is not a

constraint.

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

completing transactions. $($Round the intermediate calculations to $2$ decimal places. Round the

calculation of the service rate to the nearest whole number. Round the final answer to $1$

decimal place.$)(4$ points$)$

Average time:

minutes

b$.$ Determine the probability that a customer will not have to wait upon arrival at the ABM. $($Round the

value of $""$ to the nearest whole number. Round the final answer to $2$ decimal places.$)(3)$

Probability:

c$.$ Determine the utilization of the ABM. $($Round the value of $""$ to the nearest whole number.

Round the final answer to $2$ decimal places.$)(3)$

Utilization rate: