Question

Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities. A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the last​ century, the mean number of major hurricanes to strike a certain​ country's mainland per year was about 0.6. Find the probability that in a given year​ (a) exactly one major hurricane will strike the​ mainland, (b) at most one major hurricane will strike the​ mainland, and​ (c) more than one major hurricane will strike the mainland.

Answer 1

X ~ Poisson () = Poisson (0.6)

So,

= 0.6

P(X) = e^-X / X!

a)

P( X = 1) = e^-0.6 * 0.6

= 0.3293

b)

P( X <= 1) = P( X = 0) + P( X = 1)

= e^-0.6  + e^-0.6 * 0.6

= 0.8781

c)

P( X > 1) = 1 - P( X <= 1)

= 1 - 0.8781 (Probability calculated in part b)

= 0.1219

Since all probabilities are greater than 0.05, no event is unusual.