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 correct answer is 67%.

Explanation:

we take the number of average customers per hour multiply by hours per day to get total number of customers, then divide it by space capacity to get number customers accommodate then divide that number by total to get % of accommodated customers then we minus it on 100%

15*24 = 360 customers

360/3 = 120 accommodate

120/360*100 = 33.33%

then no place to park = 100-33.33 = 67%

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%