Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a ty

Question

Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used:

f) CEO Benjamin Neve is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. He assumes that this will cut the waiting time in half.

If a second teller is added, the average time a customer spends in the queue = .50 minutes (round your response to two decimal places).

B.) If a second teller is added, the average number of customers in the queue = ______customers (round your response to four decimal places).

C.) The average time in the system = ______ minutes (round your response to two decimal places).

D) The average number in the system = _______ customers (round your response to two decimal places).

E) The probability that the bank is empty = ________ (round your response to two decimal places).

Please answer the following questions with the second bank teller added.

Explanation / Answer

Solution:

f)

B) average number of customers in the queue   

= (1/6)*0.610294 = 0.101716 customers      

C) The average time in the system = 0.610294 + 4 = 4.610294 minutes

D) The average number in the system = 4.610294/6 = 0.7684 customers

E) The probability that the bank is empty = (1-0.333) = 66.67 %  

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