Question

10. 0/0.27 points Previous Answers BBUnderStat12 5.4.029. My Notes Ask Your Teacher In western Kansas, the summer density of hailstorms is estimated at about 1.5 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 9 square miles of Kansas wheat land against hall damage. Letr be a random variable that represents the number of hailstorms this summer in the 9-square-mile tract. (a) Explain why a Poisson probability distribution is appropriate for r. Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent, Hall storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent, Hall 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. What is for the 9-square-mile tract of land? Round , to the nearest tenth so that you can use Table 4 of Appendix II for Poisson probabilities, 1.5 (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 Pfr 2 4 1 722). (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? Computer<61-23). (Round your answer to four decimal places.) Need Help? Read it Type here to search

Answer 1

a)

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

λ =9*1.5/5=2.7

b)

P(r>=4|r>=2) =P(r>=4)/P(r>=2)=0.2859/0.7513 =0.3805

c)P(r<6|r>=3) =P(3<=r<6)/P(r>=3) =0.4496/0.5064 =0.8880