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Problem 10-6 Students arrive at the Administrative Services Ofce at an average of one every 24 minutes, and their requests take on average 20 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 1 decimal E D n m . u b. How much time, on average, does a student spend waiting in line? {Do not round intermediate calculations. Round your answer to 1 decimal place.} c. How long is the (waiting) line on average? {Round your answer to 2 decimal places.) d. What is the probability that an arriving student (just before entering the Administrative Services Office) will nd at least one other student waiting in line? {Do not round intermediate calculations. Round your answer to 4 decimal places.) Problem 10-7 Burrito King {a new fast-food franchise opening up nationwide) has successfully automated burrito production for its drive-up fast-food establishments. The Burro-Master 9000 requires a constant 40 seconds to produce a batch of burritos. It has been estimated that customers will arrive at the drive-up window according to a Poisson distribution at an average of one every 65 seconds. To help determine the amount of space needed for the line at the drive-up window a. What is the average waiting line length (in cars}? (Do not round intermediate calculations. Round your answer to 2 decimal places.) In. What is the average number of cars in the system (both in line and at the window)? (Do not round intermediate calculations. Round your answer to 2 decimal places.) c. What is the expected average time in the system, in minutes? (Do not round intermediate calculations. Round your answer to 2 decimal places.)