You are planning employees for a bank. You plan for six tellers. Tellers take 15 minutes per customer, with a standard deviation of seven minutes. Customers will arrive one every three minutes according to an exponential distribution (recall that the standard deviation is equal to the mean). Every customer who arrives eventually gets serviced.a. On average, how many customers would be waiting in line?b. On average, how long would a customer spend in the bank?c. If a customer arrived, saw the line, and decided not to get in line, that customer has ________.d. A customer who enters the line but decides to leave the line before getting service is said to have ________.
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 employees for a bank. You plan for six tellers. Tellers take 15 minutes per customer, with a standard deviation of seven minutes. Customers will arrive one every three minutes according to an exponential distribution (recall that the standard deviation is equal to the mean). Every customer who arrives eventually gets serviced.
a. On average, how many customers would be waiting in line?
b. On average, how long would a customer spend in the bank?
c. If a customer arrived, saw the line, and decided not to get in line, that customer has ________.
d. A customer who enters the line but decides to leave the line before getting service is said to have ________.
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