In western Kansas, the summer density of hailstorms is estimated at about 2.0 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. O Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent. O Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. O Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent. O Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent. What is i for the 10-square-mile tract of land? Round å 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 2 4 |r2 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 2 3). (Round your answer to four decimal places.)
In western Kansas, the summer density of hailstorms is estimated at about 2.0 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. O Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are independent. O Hail storms in western Kansas are a rare occurrence. It is reasonable to assume the events are dependent. O Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are independent. O Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent. What is i for the 10-square-mile tract of land? Round å 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 2 4 |r2 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 2 3). (Round your answer to four decimal places.)
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
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Transcribed Image Text:In western Kansas, the summer density of hailstorms is estimated at about 2.0 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.
Hail storms in western Kansas are a rare 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 independent.
Hail storms in western Kansas are a common occurrence. It is reasonable to assume the events are dependent.
What is i for the 10-square-mile tract of land? Round 1 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). (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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