Repair calls are handled by one repairman at a photocopy shop. Repair time, including traveltime, is exponentially distributed, with a mean of two hours per call. Requests for copier repairscome in at a mean rate of three per eight-hour day (assume Poisson). Determine:(1) The average number of customers awaiting repairs.(2) System utilization.(3) The amount of time during an eight-hour day that the repairman is not out on a call.(4) The probability of two or more customers in the system.c. An average of 18 customers arrive at a service center each hour. There are two servers on duty,
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel
time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs
come in at a mean rate of three per eight-hour day (assume Poisson). Determine:
(1) The average number of customers awaiting repairs.
(2) System utilization.
(3) The amount of time during an eight-hour day that the repairman is not out on a call.
(4) The probability of two or more customers in the system.
c. An average of 18 customers arrive at a service center each hour. There are two servers on duty,
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