On Friday nights, patients arrive at the emergency room at Mercy Hospital at an average rate of seven per hour, which follows a Poisson distribution. Assume that an emergency-room physician can treat an average of three patients per hour, and that the treatment times follow an exponential distribution. The board of directors for Mercy Hospital wants patients arriving at the emergency room to wait no more than five minutes before seeing a doctor.
How many emergency-room doctors should be scheduled on Friday nights to achieve the hospital’s objective?