For the past 108 years, a certain state suffered 27 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts (a) through (d). (a) What is the probability that the state will not be hit by any major hurricanes in a single year? The probability is 0.7788 . (Round to four decimal places as needed.) (b) What is the probability that the state will be hit by at least one major hurricane in a single year? The probability is 0.2212 . (Round to four decimal places as needed.) Is this unusual? Yes No (c) What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened last year? The probability is . (Round to four decimal places as needed.)
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- We know that over the past 108 years, there were 27 direct hits from major hurricanes. - We are assuming the number of hits per year follows a Poisson distribution. - We are asked to find the probability that the state will be hit by at least three major Show more…
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For the past 110 years, a certain state suffered 26 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts (a) through (d). (a) What is the probability that the state will not be hit by any major hurricanes in a single year? The probability is ________. (Round to four decimal places as needed.) (b) What is the probability that the state will be hit by at least one major hurricane in a single year? The probability is ________. (Round to four decimal places as needed.) Is this unusual? Yes No (c) What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened several years ago? The probability is ________. (Round to four decimal places as needed.) Does this indicate that the hurricane season several years ago in this state was unusual? Yes No (d) What is the probability that the state will be hit by at least two major hurricanes in a single year, as happened last year? The probability is ________. (Round to four decimal places as needed.) Does this indicate that the hurricane season this year in this state was unusual? Yes No
Madhur L.
For the past 115 years, a certain state has suffered 36 direct hits from major (category 3 to 5) hurricanes. Assume that this was typical and the number of hits per year follows a Poisson distribution. Complete parts (a) through (d). (a) What is the probability that the state will not be hit by any major hurricanes in a single year? (Round to four decimal places as needed.) (b) What is the probability that the state will be hit by at least one major hurricane in a single year? (Round to four decimal places as needed.) Is this unusual? (c) What is the probability that the state will be hit by at least three major hurricanes in a single year, as happened last year? (Round to four decimal places as needed.) Does this indicate that the 2004 hurricane season in this state was unusual?
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Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 7.3 per year. a. Find the probability that, in a year, there will be 6 hurricanes. b. In a 45-year period, how many years are expected to have 6 hurricanes? c. How does the result from part (b) compare to a recent period of 45 years in which 6 years had 6 hurricanes? Does the Poisson distribution work well here? a. The probability is . (Round to three decimal places as needed.) b. The expected number of years with 6 hurricanes is . (Round to one decimal place as needed.) c. The result from part (b) is the number of hurricanes in the recent period of 45 years, so the Poisson distribution appear to work well in the given situation.
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