Customers Arrive at the First Fidelity Bank Branch on Fridayafternoon

question 36

Essay

Customers arrive at the First Fidelity Bank branch on Fridayafternoon according to a Poisson process at a mean rate of 45 per
hour.The average time a teller takes to serve a customer is two
and a half minutes and service time follows an exponential
distribution.At present, the bank has two tellers on staff to
serve customers during this time.
A.Determine the average time a customer will wait in line before
being served.
B.Determine the probability an arriving customer will have to wait in line.
C.Determine the average number of customers in the system.
D.Suppose that the bank would like the average time a customer
spends waiting in line to be three minutes or less.What is the
fewest number of tellers they should employ to meet this goal?

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Definitions:

Extra-low Range

A gear setting in vehicles offering significantly reduced speed and increased torque for challenging terrain or heavy loads.

Solenoid Coil

An electromagnetic coil used to convert electrical energy into linear motion, often used in valves or as actuating mechanisms.

Operating Variables

Factors that can be adjusted or varied during the operation of a machine, system, or process, affecting its performance or outcome.

Fast Adaptive Mode

High-speed processing algorithms; Allison uses this term to describe an operating condition in which large changes are made to initial shift conditions to adjust for major system tolerances such as solenoid-to-solenoid, main pressure, and clutch-to-clutch variations. A new or newly rebuilt transmission should be programmed to operate in fast adaptive mode.