Coastal businesses along the Gulf of Mexico from Texas to Florida worry about the threat of hurricanes during the season from June through October. Businesses become especially nervous when hurricanes enter the Gulf of Mexico. Suppose the arrival of hurricanes during this season is Poisson distributed, with an average of three hurricanes entering the Gulf of Mexico during the five-month season. If a hurricane has just entered the Gulf of Mexico:

a. What is the probability that at least one month will pass before the next hurricane enters the Gulf?

b. What is the probability that another hurricane will enter the Gulf of Mexico in two weeks or less?

c. What is the average amount of time between hurricanes entering the Gulf of Mexico?