In a 24-hour call center, complaints arrive at a mean rate of 1 complaint every 3 hours. (a) Find the probability that there are at most 3 complaints in the past 10 hours. (b) A day is “doomed” if...

In a 24-hour call center, complaints arrive at a mean rate of 1 complaint every 3 hours.

(a) Find the probability that there are at most 3 complaints in the past 10 hours.

(b) A day is “doomed” if there are at least 6 complaints. Each day, an inspector counts the number of complaints at the end of the day and determines whether the day was doomed. Find the probability that the inspector has worked for 7 days when he records the 3rd doomed day.

(c)  Find the probability that there are at least 2 complaints in the past 12 hours given that there are at most 5 complaints in the past 12 hours