Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.e. What is the probability that there are fewer than two customers in the bakery?
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!
Customers arrive to a local bakery with an average time between arrivals of
5 minutes. However, there is quite a lot of variability in the customers’ arrivals, as
one would expect in an unscheduled system. The single bakery server requires an
amount of time having the exponential distribution with mean 4.5 minutes to serve
customers (in the order in which they arrive). No customers leave without service.
e. What is the probability that there are fewer than two customers in the bakery?
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