In western Kansas, the summer density of hailstorms is estimated at about 2.6 storms per 5 square miles. In most cases, a hailst
orm damages only a relatively small area in a square mile. A crop insurance company has insured a tract of 8 square miles of Kansas wheat land against hail damage. Let r be a random variable that represents the number of hailstorms this summer in the 8-square-mile tract. (a) Explain why a Poisson probability distribution is appropriate for r.
Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent.Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent.
What is λ for the 8-square-mile tract of land? Round λ to the nearest tenth so that you can use Table 4 of Appendix II for Poisson probabilities.
(b) If there already have been two hailstorms this summer, what is the probability that there will be a total of four or more hailstorms in this tract of land? Compute P(r≥ 4 | r ≥ 2). (Use 4 decimal places.)
(c) If there already have been three hailstorms this summer, what is the probability that there will be a total of fewer than six hailstorms? Compute P(r < 6 | r ≥ 3). (Use 4 decimal places.)
I see the question last and the 4 choices first. Look at the points you have in the table with the question. (0, 0), (4, 2), (9, 3) The only graph that contains those three points is the second option.