(a) Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an average of 10 units per hour. The service time is distributed exponentially with a mean of 3 minutes. Find the following: iv. Probability that a customer arriving at the pump will have to wait v. The utilization factor for the pump unit vi. Probability that the number of customers in the system is 2.
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) Auto vehicles arrive at a petrol pump, having one petrol unit, in Poisson fashion with an
average of 10 units per hour. The service time is distributed exponentially with a mean of
3 minutes. Find the following:
iv. Probability that a customer arriving at the pump will have to wait
v. The utilization factor for the pump unit
vi. Probability that the number of customers in the system is 2.
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