Automobiles arrive at the$$drive$-$through window at the downtown Baton$$Rouge$,$ Louisiana, post office at the rate of

$2$

every $10$ minutes. The average service time is

$1\mathrm{.}0$

minutes. The Poisson distribution is appropriate for the arrival rate and service times are negative exponentially distributed.

Part $2$

$$a$)$ The average time a car is in the system$=$

$1\mathrm{.}25$

minutes$($round your response to two decimal$$places$).$

Part $3$

$$b$)$ The average number of cars in the system$=$

$0\mathrm{.}25$

cars$($round your response to two decimal$$places$).$

Part $4$

$$c$)$ The average number of cars waiting to receive service$=$

$0\mathrm{.}05$

cars$($round your response to two decimal$$places$).$

Part $5$

$$d$)$ The average time a car is in the queue$=$

$0\mathrm{.}25$

minutes$($round your response to two decimal$$places$).$

Part $6$

$$e$)$ The probability that there are no cars at the window$=$

$0\mathrm{.}80$

$($round your response to two decimal$$places$).$

Part $7$

$$f$)$ The percentage of the time the postal clerk is busy$=$

$20\%$

$($round your response to the nearest whole$$number$).$

Part $8$

$$g$)$ The probability that there are exactly $2$ cars in the system$=$

$0\mathrm{.}032$

$($round your response to three decimal$$places$).$

Part $9$

$$h$)$ If a second$$drive$-$through window, with its own$$server$,$ were$$added$,$

the

average time a car is in the system$=$

enter your response here

minutes$($round your response to two decimal$$places$).$