Willow Brook National Bank operates a drive$-$up teller window that allows

customers to complete bank transactions without getting out of their cars. On weekday mornings,

arrivals to the drive$-$up teller window occur at random, with an arrival rate of $24$ customers per

hour or $0\mathrm{.}4$ customers per minute. Assume the Poisson probability distribution can be used to

describe the arrival process and the Exponential probability distribution with a service rate of $36$

customers per hour, or $0\mathrm{.}6$ customers per minute to describe the service times for the drive$-$up

teller. Use the single$-$server drive$-$up bank teller operation to determine the following operating

characteristics for the system $($use formulas and show all your work$)$:

a$)(1\mathrm{.}5$ pts$)$ The probability that no customers are in the system.

b$)(1\mathrm{.}5$ pts$)$ The average number of customers waiting.

c$)(1\mathrm{.}5$ pts$)$ The average number of customers in the system.

d$)(1\mathrm{.}5$ pts$)$ The average time a customer spends waiting.

e$)(1\mathrm{.}5$ pts$)$ The average time a customer spends in the system.

f$)(1\mathrm{.}5$ pts$)$ The probability that arriving customers will have to wait for service $($utilization

rate$).$