Final answer:
The expected wait time in the bank, where the service rate is 30 customers per hour, is two minutes between successive customers. For three customers, the average time will be six minutes.
Step-by-step explanation:
In an exponential distribution with an average service rate of 30 customers per hour, we can find the expected wait time in the bank. Given that there are 60 minutes in an hour, and the service rate is 30 customers per hour, we can determine that on average there is one customer every two minutes. Therefore, to find the expected wait time or the average time between two successive arrivals, we simply divide the total time in an hour by the number of customers served in that hour which equals two minutes per customer.
Expected wait time is thus the average time between the arrival of one customer and the next in this context. If we are interested in finding out how long it takes, on average, for a certain number of customers to be served, we multiply the expected wait time by the number of customers. For example, it takes six minutes on average for three customers to arrive since six is the product of the expected wait time (two minutes) and the number of customers (three).