A bank facility has space for 3 cars in its single drive thru lane. If an average of 15 customers drive to the bank to use the drive thru ATM per hour, and if it takes an average of 3 minutes for a customer to complete the service at the ATM, what percentage of customers wanting to use the drive thru ATM will not have a place to park in the lane before service? a. 68% b. 32% c. 10% d. 90%

The percentage of customers wanting to use the drive thru ATM and will not have a place to park in the lane before service is 4.5%

Explanation:

Arrival rate (Ar) = 15 per hour

Service rate (Sr) = 3 minutes for a customer, which is 20 customers per hour

M = 3

Lq = 0.015

Wq = Lq/Ar = 0.015/15 = 0.001

Wa = 1/(M*Sr - A) = 1/(3*20 -15) = 0.022

Probability of waiting in the system = Wq/Wa = 0.001/0.022 = 0.045 or 4.5%

answer; is usually (less than) the socially optimal level of consumption;