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Suppose that the hurricane record over a 10-year period at a certain coastal city in Florida is as follows.
Suppose that the hurricane record over a 10-year period at a certain coastal city in Florida is as follows.
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The occurrence of hurricanes can be described by a Poisson process. The maximum wind speed of hurricanes shows considerable fluctuation. Suppose that those recorded in this city can be fitted satisfactorily by a lognormal distribution with mean = 100 ft/sec and standard deviation = 20 ft/sec.
a) Based on the available data, find the probability that there will be at least 1 hurricane in this city in the next 2 years.
b) If a structure in this city is designed for a wind speed of 130 ft/sec, what is the probability that the structure will be damaged (design wind speed exceeded) by the next hurricane?
c) What is the probability that there will be at most 2 hurricanes in the next 2 years, and that no structure will be damaged during this period?
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