Question

Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 83 seconds completing his or her transactions. Transaction time is exponentially distributed.

a. Determine the average time customers spend at the machine, including waiting in line and completing transactions. (Do not round intermediate calculations. Round your answer to the nearest whole number.)
  
Average time ______   minutes

b. Determine the probability that a customer will not have to wait upon arriving at the automatic teller machine. (Round your answer to 2 decimal places.)
  
Probability ______

c. Determine the average number of customers waiting to use the machine. (Round your answer to 2 decimal places.)
  
Average number ______ customers

Answer 1

ANSWER:     Arrival rate = 30 per hour

Service rate = 43.37 per hour

a)

Average time customers spend at the machine W

W=1(/service rate-Arrival rate)

W = 1/ (43.37-30) = 0.075 hours or 4.49 minutes

b) The probability that a customer will not have to wait upon arriving at the automatic teller machine=   1-Arrival rate/service rate    

1-30/43.37 =0.31

Probability= 0.31