Students arrive at the Administrative Services Office at an average of one every $10$ minutes $,$ and their requests take $,$ on average $7\mathrm{.}5$ minutes to be processed $.$ The service counter is staffed by only one clerk, Judy Gumshoes $,$ who works eight hours per dayAssume Poisson arrivals and exponential service times a$.$ What percentage of time is Judy $?$ Note: Round your answer to $1$ decimal place Percentage of time bHow much time, on average, does a student spend in line? Note: Do not round intermediate calculations. Round your answer to $1$ decimal place. Average time minutes How long is the $($waiting$)$ line on average? Note: Round your answer to $2$ decimal places customers Average length of the waiting d $.$ What is the probability that an arriving student $($just before entering the Administrative Services Office $)$ will find at least one other student waiting in line? Note: Do not round intermediate calculations $.$ Round your answer to $2$ decimal places $\%$ Probability There is a $2$ percent error rate at a specific point in a production process an inspector is placed at this point $,$ all the errors can bedetected and eliminated $.$ However $,$ the inspector is paid $$11$ per hour and can inspect units the process at the rate of $53$ per hour If no inspector is used and defects are allowed to pass this point, there is a cost of $ $10$ per unit to correct the defect later on Assume that the line will operate at the same rate $($the current production rate$)$ regardless of whether the inspector is hired or not. a$.$ If an inspector is hired $,$ what will be the inspection cost per unit? Note: Round your answer to $3$ decimal places. Cost per unit bIf an inspector is not hired, what will be the defective cost per unit? Note: Round your answer to $3$ decimal places. Cost per unit $.$ Should an inspector be hired based on costs alone? No Yes