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

Question 5.46

5.46 Email.

Suppose the average number of emails received by a particular employee at your company is five emails per hour. Suppose the count of emails received can be adequately modeled as a Poisson random variable. Compute the following probabilities without the aid of software.

  1. What is the probability of this employee receiving exactly five emails in any given hour?
  2. What is the probability of receiving less than five emails in any given hour?
  3. What is the probability of receiving at least one email in any given hour?
  4. What is the probability of receiving at least one email in any given 30-minute span?