Neve Commercial Bank is the only bank in the town of$$ York, Pennsylvania. On a typical$$ Friday, an average of $10$ customers per hour arrive at the bank to transact business. There is one teller at the$$ bank, and the average time required to transact business is $4$ minutes. It is assumed that service times may be described by the negative exponential distribution. A single line would be$$ used, and the customer at the front of the line would go to the first available bank teller. If a single teller is$$ used:

Part $2$

$$a$)$ The average time in the line$=8\mathrm{.}008\mathrm{.}00$ minutes$($round your response to two decimal$$ places$).$

Part $3$

$$b$)$ The average number in the line$=1\mathrm{.}331\mathrm{.}33$ customers$($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ The average time in the system$=12\mathrm{.}0012\mathrm{.}00$ minutes$($round your response to two decimal$$ places$).$

Part $5$

$$d$)$ The average number in the system$=2\mathrm{.}002\mathrm{.}00$ customers$($round your response to two decimal$$ places$).$

Part $6$

$$e$)$ The probability that the bank is empty$=0\mathrm{.}330\mathrm{.}33($round your response to two decimal$$ places$).$

Part $7$

$$f$)$ CEO Benjamin Neve is considering adding a second teller$($who would work at the same rate as the$$ first$)$ to reduce the waiting time for customers. He assumes that this will cut the waiting time in half.

Part $8$

If a second teller is$$ added, the average time a customer spends in the queue$=0\mathrm{.}600\mathrm{.}60$ minutes$($round your response to two decimal$$ places$).$

Part $9$

If a second teller is$$ added, the average number of customers in the queue$=0\mathrm{.}10000\mathrm{.}1000$ customers$($round your response to four decimal$$ places$).$

Part $10$

If a second teller is$$ added, the average time a customer spends in the system$=4\mathrm{.}504\mathrm{.}50$ minutes$($round your response to two decimal$$ places$).$

Part $11$

If a second teller is$$ added, the average number of customers in the system$=0\mathrm{.}7500\mathrm{.}750$ customers$($round your response to three decimal$$ places$).$

Part $12$

If a second teller is$$ added, the probability that the bank is empty$=$ enter your response here $($round your response to two decimal$$ places$).$