Question: Customers arrive at a bank at the mean rate of 15 per hour. The exponential probability distribution describes the time between customer arrivals.

a) The customer service manager thinks that if a customer arrives within 3 minutes of a previous customer, a new teller must be added. What is the probability that it will occur?

b) What is the probability that the bank will go 6 minutes without a customer arrival?

Make sure you show your work and explain each answer. Use Ph.Stat for calculations.