Please solve and show work.

1. Students arrive at the Administrative Services Office at an average of one every 12 minutes, and their requests take on average 10 minutes to be processed. The service counter is staffed by only one clerk, Judy Gumshoes, who works eight hours per day. Assume Poisson arrivals and exponential service times. a. What percentage of time is Judy idle? (Round your answer to 2 decimal places.) b. How much time, on average, does a student spend waiting in line? (Round your answer to the nearest whole number.) c. How long is the (waiting) line on average? (Round your answer to 2 decimal places.) 2. To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on the average, 10 persons per hour request a test. Assume arrivals are Poisson from an infinite population. Blood pressure measurements can be made at a constant time of three minutes each. Assume the queue length can be infinite with FCFS discipline. a. What average number in line can be expected? (Round your answer to 4 decimal places.) b. What average number of persons can be expected to be in the system? (Round your answer to 4 decimal places.) c. What is the average amount of time that a person can expect to spend in line? (Round your answer to 4 decimal places.) d. On the average, how much time will it take to measure a person's blood pressure, including waiting time? (Round your answer to 4 decimal places.)