There is only one copying machine in the student lounge of the business school. Students arrive at the rate of $\backslash$lambda $=40$ per hour $($according to a Poisson distribution$).$ Copying takes an average of $45$ seconds, or $\backslash$mu $=80$ per hour $($according to a negative exponential distribution$).$ a$)$ The percentage of time the machine is used $=$ enter your response here percent $($round your response to the nearest whole number$).$ b$)$ The average length of the queue $=$ enter your response here students $($round your response to two decimal places$).$ c$)$ The average number of students in the system $=$ enter your response here students $($round your response to two decimal places$).$ d$)$ The average time spent waiting in the queue $=$ enter your response here minutes $($round your response to two decimal places$).$ e$)$ The average time in the system $=$ enter your response here minutes $($round your response to two decimal places$).$