cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed. e. If the cafeteria
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!
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 three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed.
e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 15 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? (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 15 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time? (Round your answer to 2 decimal places.)
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