Question: A business convention holds its registration on Wednesday morning from 9:00 A.M. until 12:00 noon Past history has shown that registrant arrivals follow a Poisson distribution at an average rate of 1.8 every 15 seconds. Fortunately, several facilities are available to register convention members.
a. What is the average number of seconds between arrivals to the registration area for this conference based on past results?
b. What is the probability that 25 seconds or more would pass between registration arrivals?
c. What is the probability that less than five seconds will elapse between arrivals?
d. Suppose the registration computers went down for a one-minute period. Would this condition pose a problem? What is the probability that at least one minute will elapse between arrivals?