A large automotive repair shop has instituted a system for mechanics to check out the needed supplies from the Parts Department. Observation of the system has shown that the rate of arrivals of mechanics (who are internal customers in this setting) to check out supplies follows a Poisson distribution with an average rate of 10 per hour. It takes an average of 5 minutes to get the supplies to the mechanic and these times follow an exponential distribution. Assume that there is currently only one person working at the service window in the parts department. The hourly salary of the service attendant (resource unit) is 30$ and the hourly salary of the mechanic is $40. What is the total system time cost?
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!
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