The time between people arriving to a softball game in a window of time is distributed as an exponential random variable with mean 0.2 minutes. a. What is the expected number of people arriving per hour? b. What is the probability that a ticket-checker has to wait at least 2 minutes between two consecutive arrivals? c. A ticket-checker has waited for 3 minutes without an arrival. What is the probability that they have to wait at least 2 more minutes?

Airline passengers arrive randomly and independently at the passenger screening facility at a major international airport. The mean arrival rate is 5 passengers per minute. 1. What is the probability of 2 arrivals in a 1-minute period? 2. What is the probability of no arrivals in a 1-minute period? 3. What is the probability of one arrival in a 1-minute period? 4. What is the probability of at most one arrival in a 1-minute period?

Q3. A 10-year record of tornadoes per year to land in a particular region is 2, 2, 1, 3, 2, 1, 0, 2, 3, and 1. Using Poisson's distribution, what is the probability of not having tornados in any 1 year? What are the average of the number of tornadoes in 1 year?

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport. The mean arrival rate is 11 passengers per minute. a. Compute the probability of no arrivals in a one-minute period (to 6 decimals). 0.0000 b. Compute the probability that three or fewer passengers arrive in a one-minute period (to 4 decimals). 0.0103 c. Compute the probability of no arrivals in a 15-second period (to 4 decimals). 0.0820 d. Compute the probability of at least one arrival in a 15-second period (to 4 decimals). 0.9179