Unless stated otherwise in the exercise, use software to find the exact Poisson.

Question 5.44

5.44 How many calls?

Calls to the customer service department of a cable TV provider are made randomly and independently at a rate of 11 per minute. The company has a staff of 20 customer service specialists who handle all the calls. Assume that none of the specialists are on a call at this moment and that a Poisson model is appropriate for the number of incoming calls per minute.

  1. What is the probability of the customer service department receiving more than 20 calls in the next minute?
  2. What is the probability of the customer service department receiving exactly 20 calls in the next minute?
  3. What is the probability of the customer service department receiving fewer than 11 calls in the next minute?