Ship collisions in the Houston Ship Channel are rare. Suppose the numbers of collisions are Poisson distributed, with a mean of 1.2 collisions every four months.
a. What is the probability of having no collisions occur over a four-month period?
b. What is the probability of having exactly two collisions in a two-month period?
c. What is the probability of having one or fewer collisions in a six-month period? If this outcome occurred, what might you conclude about ship channel conditions during this period? What might you conclude about ship channel safety awareness during this period? What might you conclude about weather conditions during this period? What might you conclude about lambda?