In western Kansas, the summer density of hailstorms is estimated at about 2.2 storms per 5 square miles. In most cases, a

Question

In western Kansas, the summer density of hailstorms is estimated at about 2.2 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square
insurance company has insured a tract of 10 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 10-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 independent.
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 dependent.
Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent.
What is λ for the 10-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(r24|r≥ 2). (Round
your answer to four 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). (Round your answer to four
decimal places.)

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