Question

At a fashion retailer, there are three cashiers providing checkout service simultaneously. On average, customers arrive at the checkout area every 6 minutes. It is estimated that the customer arrival process is a Poisson process. The average checkout time for each customer is 12 minutes, with its standard deviation equal to 20 minutes. Suppose that customers form a single line. What is the average waiting time in minutes for a customer?

Answer 1

The average waiting time for a customer is 6 minutes.

Step-by-step explanation:

To find the average waiting time for a customer, we need to consider both the average arrival rate and the average checkout time. In this case, the average arrival rate is given as one customer every 6 minutes. We can calculate the average service rate by taking the reciprocal of the average checkout time, which is 1/12 (since it takes 12 minutes on average to serve one customer).

Using the formula for the average waiting time in a queue, which is given by W = (1 / service rate) - (1 / arrival rate), we can substitute the values to find the average waiting time:

W = (1 / (1/12)) - (1 / (1/6)) = 12 - 6 = 6 minutes

Therefore, the average waiting time for a customer is 6 minutes.