The average transaction at an automatic teller can be completed in 7.5 minutes and customers arrive at the average rate of one every ten minutes.On average,how many customers are there in line? (Choose the closest answer. )
A)4.000 Customers
B)0.300 Customers
C)3.000 Customers
D)0.375 Customers

Question

The average transaction at an automatic teller can be completed in 7.5 minutes and customers arrive at the average rate of one every ten minutes.On average,how many customers are there in line? (Choose the closest answer. )
A)​4.000 Customers
B)​0.300 Customers
C)​3.000 Customers
D)​0.375 Customers

Quizplus · Accepted Answer

We can use the M/M/1 queuing model to solve the problem. The arrival rate is 1 customer every 10 minutes, and the service rate is 1 customer every 7.5 minutes. The utilization factor (rho) is then calculated as 0.75. Using the formula for the expected number of customers in a queuing system, we get Lq = (rho^2)/(1-rho) = 3. Therefore, on average, there are 3 customers in line. The closest answer choice is C, 3.

The Average Transaction at an Automatic Teller Can Be Completed