According to studies by VHA Inc., an alliance of community hospitals, on average, it takes 49 minutes before a doctor sees a patient in a U.S. emergency room.
One hospital, Oakwood Medical Center in Dearbom, Michigan, promises that anybody taken to the emergency department would be seen by a doctor within 30 minutes - or they would get a written apology and two free movie passes.
To reduce emergency room waiting times, the hospital improved patient check-in procedures, billing, record keeping, and laboratory processes. Acute-care beds are set aside for the real emergencies and an adjacent "fast track" section is designed to treat lesser emergencies to get patients treated and released quickly.
One of the performance measures tracked by the hospital revealed that only 0.8% of the 191,000 emergency room patients (about 1,700 people) were eligible for free tickets. Given this level of performance, what is the probability that 1 or fewer customers in the next 20 (n = 20) will have to wait longer than 30 minutes? In other words, what is the probability that l or fewer customers will receive free tickets?