What is the probability that an arriving student

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Students arrive at the Administrative Services Office 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 place.)

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 find at least one other student waiting in line? (Do not round intermediate calculations. Round your answer to 4 decimal places.)

2. 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 9,000 requires a constant 50 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 60 seconds.

a. What is the average waiting line length (in cars)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. 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.)

3. 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 average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of four 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 3 decimal places.)

b. What average number of persons can be expected to be in the system? (Round your answer to 3 decimal places.)

c. What is the average amount of time a person can expect to spend in line? (Round your answer to 4 decimal places.)

d. On average, how much time will it take to measure a person's blood pressure, including waiting time? (Round your answer to 4 decimal places.)

4.A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 12 seconds, exponentially distributed.

a. How many customers would you expect to see, on average, at the coffee urn? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

b. How long would you expect it to take to get a cup of coffee? (Round your answer to 2 decimal places.)

c. What percentage of time is the urn being used? (Do not round intermediate calculations. Round your answer to 1 decimal place.)

d. What is the probability that three or more people are in the cafeteria? (Round your intermediate calculations to 3 decimal places and final answer to 1 decimal place.)

e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 12 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

f. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 12 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Reference no: EM133447906

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