Question 3 (10 points) a. (5 points) Suppose that a bank has one Automatic Teller Machine. Customers arrive at the Machine at a rate of 5 per ¼ hour. Assume a Poisson distribution. 1. What is the probability that no one will arrive in a 15-minute interval (1/4 hour)? 2. What is the probability that at least 3 persons will use a teller machine in a 15-minute interval? b. (5 points) You manage a plant that produces processors for mobile phones. On average 5 processors fail per week. Assume a Poisson Distribution 1. What is the probability that up to 6 processors fail this week? 2. What is the probability that between 7 and 10 processors fail?