There is only one copying machine in the student lounge of the business school. Students arrive at the rate of

per hour$($according to a Poisson$$ distribution$).$ Copying takes an average of $$seconds$,$ or per hour$($according to a negative exponential$$ distribution$).$

Part $2$

$$a$)$ The percentage of time the machine is used$=$

$$

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

Part $3$

$$b$)$ The average length of the queue$=$

$$

enter your response here students$($round your response to two decimal$$ places$).$

Part $4$

$$c$)$ The average number of students in the system$=$

$$

enter your response here students$($round your response to two decimal$$ places$).$

Part $5$

$$d$)$ The average time spent waiting in the queue$=$

$$

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

Part $6$

$$e$)$ The average time in the system$=$

$$

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