Suppose that the average number of calls arriving at the switchboard of a corporation is 30 calls per hour. Assume that the number of calls arriving during any time period has a Poisson distribution and assume the time is measured in minutes. Therefore, 30 calls per hour is 0.5 calls per minute, so that the mean rate of occurrence is 0.5 calls per minute. Solve the following points.

a. What is the probability that no calls will arrive in 3-minute period? (Hint: in this case l ¼ 0:5,3 and P[No calls in 3 min period] ¼ e  vt y 0.223).

b. What is the probability that more than five calls will arrive in a 5-minute interval?

c. Plot the Poisson distribution for each case.