From 3:00 P.M. to 8:00 P.M. the local K-Star Supermarket has a steady stream of customers. Customers finish shopping and arrive at the checkout area at a rate of 70 per hour (Poisson distributed).It is assumed that when customers arrive at the cash registers, they will divide themselves relatively evenly so that all the checkout lines contain an equal number. The average checkout time at a register is 7 minutes (exponentially distributed). The store manager’s service goal is for customers to be out of the store within 12 minutes (on average) after they complete their shopping and arrive at a cash register. How many cash registers must the store have open to achieve the manager’s service goal?
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!
From 3:00 P.M. to 8:00 P.M. the local K-Star Supermarket has a steady stream of customers. Customers
finish shopping and arrive at the checkout area at a rate of 70 per hour (Poisson distributed).It is assumed that when customers arrive at the cash registers, they will divide themselves relatively
evenly so that all the checkout lines contain an equal number. The average checkout time at a register
is 7 minutes (exponentially distributed). The store manager’s service goal is for customers to
be out of the store within 12 minutes (on average) after they complete their shopping and arrive at
a cash register. How many cash registers must the store have open to achieve the manager’s service
goal?
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