The arrival of patients in a hospital follows the Poisson process at a rate of 8 people/hour.

a. Find the probability that 5 patients present in the first hour

b. What is the probability that the time between arrivals for the 4th and 5th patients is more than 1/2 hour?

c. What is the probability that the arrival time of the second patient is more than 1 hour? What is the mean and variance of the time until the arrival of the 8th patient?