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 0.48. 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. ​(a) P(exactly one major hurricane will strike the ​mainland)equals nothing ​(Round to three decimal places as​ needed.)

Answer 1

X ~ poi ( )

Where = 0.48

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

a)

P(X = 1) = e^-0.48 * 0.48

= 0.297

Since this probability is greater than 0.05, this event is not unusual.

b)

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

= e^-0.48  +e^-0.48 * 0.48

= 0.919

Since this probability is greater than 0.05, this event is not unusual.

c)

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

= 1 - 0.919

= 0.081

Since this probability is greater than 0.05, this event is not unusual.