Find the indicated probablies using the geometric distribution, the Poisson dist

Question

Find the indicated probablies using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine if the events are unusual. If convenient, use the appropriate probablity table or technology to find the probabilities major hurricanes to strike a certain major A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. Durning the last century, the mean number of country's mainland per hurricane wil strike the mainland, and (c) more than one major hurricane will strike the mainland ryear was about 047. Find the probability that in a given year (a) exactly one major hurricane will strike the mainland. (b) at most one (a) P(exactly one major humane will strike the mainland- Round to three decimal places as needed.) (b) Plat most one major hurricane will strike the mainland) (Round to three decimal places as needed.) (c) P(more than one major hurricane wil strike the mainland- Round to three decimal pliaces as needed.) Which of the events are unusual? Select al that apply A. The event in part (a) is unusual B. The event in part (b) is unusual. C. The event in part (c) is unusual D. None of the events are unusual

Explanation / Answer

= 0.47

P(X = x) = e- * x / x!

a) P(X = 1) = e-0.47 * 0.471 / 1! = 0.294

b) P(X < 1) = P(X = 0) + P(X = 1) = e-0.47 * 0.470 / 0! + e-0.47 * 0.471 / 1! = 0.919

c) P(X > 1) = 1 - P(X < 1) = 1 - 0.919 = 0.081

d) Option-C) beausethe probability is less than 0.05.

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