Students arrive one at a time, completely at random, to an advice clinic at a rate of10 per hour. Students take on average 5 minutes of advice but there is wide variation inthe time they need; this variation may be well modeled by the exponential distribution.a. Assume there is only one advisor serving in the clinic. Find the followingexpected measures of performance for this system: the expected time in the clinic, theexpected time in the queue for advice, the expected number of students in the clinic,and the expected number of students waiting for advice.
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!
Students arrive one at a time, completely at random, to an advice clinic at a rate of
10 per hour. Students take on average 5 minutes of advice but there is wide variation in
the time they need; this variation may be well modeled by the exponential distribution.
a. Assume there is only one advisor serving in the clinic. Find the following
expected measures of performance for this system: the expected time in the clinic, the
expected time in the queue for advice, the expected number of students in the clinic,
and the expected number of students waiting for advice.
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