Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 2.5 hours per call. Requests for copier repairs come in at a mean rate of 2.0 per eight-hour day (assume Poisson). Determine the following: a. The average number of customers awaiting repairs. (Round your answer to 2 decimal places.) b. System utilization. (Round your answer to 2 decimal places.) c. The amount of time during an eight-hour day that the repairman is not out on a call. (Round your answer to 2 decimal places.) d. The probability of two or more customers in the system. (Do not round intermediate calculations. Round your answer to 4 decimal places.)
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 2.5 hours per call. Requests for copier repairs come in at a mean rate of 2.0 per eight-hour day (assume Poisson). Determine the following:
a. The average number of customers awaiting repairs. (Round your answer to 2 decimal places.)
b. System utilization. (Round your answer to 2 decimal places.)
c. The amount of time during an eight-hour day that the repairman is not out on a call. (Round your answer to 2 decimal places.)
d. The probability of two or more customers in the system. (Do not round intermediate calculations. Round your answer to 4 decimal places.)
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