A self service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes. While the cashier can serve 10 customers in 5 minutes. Assuming poisson distribution for the arrival rate and exponential distribution for service time. Find (a) Average number of customers in the system. (b) Average number of customers in the queue or average queue length. (c) Average time, a customer spends in the system. (d) Average time, a customer waits before being served.
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 self service store employs one cashier at its counter. Nine customers arrive on an average every 5 minutes. While the cashier can serve 10 customers in 5 minutes. Assuming poisson distribution for the arrival rate and exponential distribution for service time. Find
(a) Average number of customers in the system.
(b) Average number of customers in the queue or average queue length.
(c) Average time, a customer spends in the system.
(d) Average time, a customer waits before being served.
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