Final answer:
On average, customers wait for 5 minutes in line at the bank. This is calculated using the arrival rate (2 customers/minute) and the average number of people in line (10).
Step-by-step explanation:
The student is asking how long bank customers wait in line given that the average number of people waiting in line is 10 and on average 2 people per minute leave the bank after receiving service. To find the average wait time for customers, we will use the information given about the rate at which customers are served.
First, we know that 2 people leave per minute, which is the service rate. This implies that each person is served in ½ a minute on average. To find out how long the average customer waits we use the formula for the average time a customer spends in the system (waiting time plus service time), which is L = λW, where L is the average number of customers in the system, λ is the arrival rate (customers per minute), and W is the average time a customer spends in the system.
Since the average number of people in line (L) is 10 and we want to find W, we need to calculate the arrival rate λ. λ can be found by taking the inverse of the service time for each customer, which is 2 customers per minute. Therefore, λ = 2. Plugging the values into the formula we get W = L/λ = 10/2 = 5 minutes. So, on average, customers wait for 5 minutes in line.