The cafeteria line in the university student center is a$$ self$-$serve facility in which students select the items they want and then form a single line to pay the cashier. Students arrive at a rate of about four per minute according to a Poisson distribution. The single cashier takes about $12$ seconds per$$ customer, following a negative exponential distribution.

Part $2$

$$a$)$ The probability there are more than two students in the system is enter your response here $($round your response to three decimal$$ places$).$

Part $3$

The probability there are more than three students in the system$=$enter your response here $($round your response to three decimal$$ places$).$

Part $4$

The probability there are more than four students in the system$=$enter your response here $($round your response to three decimal$$ places$).$

Part $5$

$$b$)$ The probability that the system is empty is enter your response here $($round your response to one decimal$$ place$).$

Part $6$

$$c$)$ Before reaching the$$ cashier, the average student have to wait enter your response here minutes $($round your response to one decimal$$ place$).$

Part $7$

$$d$)$ The expected number of students in the queue is enter your response here students $($round your response to one decimal$$ place$).$

Part $8$

$$e$)$ The average number of students in the system is enter your response here students $($enter your response as a whole$$ number$).$

Part $9$

$$f$)$ A second cashier is added and works at the same pace. Assume customers wait in a single line and go to the first available cashier.

The probability that the two server system is empty is enter your response here $($round your response to three decimal$$ places$).$

Part $10$

The average waiting time for the two server system is enter your response here minutes $($round your response to three decimal$$ places$).$

Part $11$

The average number of students in the queue for the two server system is enter your response here students $($round your response to three decimal$$ places$).$

Part $12$

The average number of students in the two server system is enter your response here students $($round your response to three decimal$$ places$).$