Question

Neve Commercial Bank is the only bank in the town of York, Pennsylvania. On a typical Friday, an average of 10 customers per hour arrive at the bank to transact business. There is currently one teller at the bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the exponential distribution. If a single teller is used, find:

The average time in the line.

Answer 1

On average, a customer arrives every 6 minutes, so it will take approximately 18 minutes for three customers to arrive at the bank.

Step-by-step explanation:

The question involves calculating the average time a customer spends in the line at the Neve Commercial Bank in York, Pennsylvania, when the inter-arrival times follow an exponential distribution.

a. Given that there are 10 customers per hour, the average time between two successive arrivals, which can be found by dividing one hour (60 minutes) by the average number of arrivals per hour (10 customers), is 6 minutes. We expect one customer every 6 minutes on average.

b. Since customers arrive every 6 minutes on average, for three customers to arrive at the store, it will take 3 times 6 minutes, which is 18 minutes on average.