6 Between 7 p.m. and 11 p.m., arrivals of patients at the casualty department of a hospital occur at random at an average rate of 6 per hour.
- Find the probability that, during any period of one hour between 7 p.m. and 11 p.m., exactly 5 people will arrive.
- A patient arrives at exactly 10.15 p.m. Find the probability that at least one more patient arrives before 10.35 p.m.
- Use a suitable approximation to estimate the probability that fewer than 20 patients arrive at the casualty department between 7 p.m. and 11 p.m. on any particular night.