Question

In western Kansas, the summer density of hailstorms is estimated at about 2.3 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop 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. Hailstorms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent. (b) 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. (c) If there have already 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). (Round your answer to four decimal places.) (d) If there have already 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.)

          In western Kansas, the summer density of hailstorms is estimated at about 2.3 storms per 5 square miles. In most cases, a hailstorm damages only a relatively small area in a square mile. A crop 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.

Hailstorms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent.

(b) 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.

(c) If there have already 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). (Round your answer to four decimal places.)

(d) If there have already 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.)

Added by Josefina Y.

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