Please Answer all Parts

4. (20 points) You work part time at a call center from 9 AM to 11 AM. During these morning hours, on average, they receive one call every two minutes. Suppose the number of arriving phone calls during the time window can be modeled by a Poisson distribution. (a) What is the probability that the call center receives less than 3 calls in the rst 5 minutes of your shift? Compute THREE DIGITS AFTER THE DECIMAL POINT. (b) Suppose the call center received 0 calls in the rst 5 minutes of your shift. What is the probability they receive less than 3 calls in the next 5 minutes? (0) What is the probabilily that the time until the fth call of the shift is longer than 5 minutes? You must use the following hint in your answer. Hint: / ew/Mac = 26_\"/2(x3 + 6332 + 245: + 48) + (constant)