You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows for the three different classes of service. Each class of service would be separate, with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. Peoplefor one class of service arrive every four minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes seven minutes to service each customer, and the standard deviation of the service times is three minutes. You assign two cashiers to each type of service.a. On average, how long will each line be at each of the cashier windows?b. On average, how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is complete)?You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times.c. What will happen to the amount of time each cashier spends idle? (increase, decrease, stay the same, depend on ________)d. What will happen to the average amount of time a customer spends in the bank? (increase, decrease, stay the same, depend on ________)
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!
You are planning the new layout for the local branch of the Sixth Ninth Bank. You are considering separate cashier windows for the three different classes of service. Each class of service would be separate, with its own cashiers and customers. Oddly enough, each class of service, while different, has exactly the same demand and service times. People
for one class of service arrive every four minutes and arrival times are exponentially distributed (the standard deviation is equal to the mean). It takes seven minutes to service each customer, and the standard deviation of the service times is three minutes. You assign two cashiers to each type of service.
a. On average, how long will each line be at each of the cashier windows?
b. On average, how long will a customer spend in the bank (assume they enter, go directly to one line, and leave as soon as service is complete)?
You decide to consolidate all the cashiers so they can handle all types of customers without increasing the service times.
c. What will happen to the amount of time each cashier spends idle? (increase, decrease, stay the same, depend on ________)
d. What will happen to the average amount of time a customer spends in the bank? (increase, decrease, stay the same, depend on ________)
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