Question

A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century, the mean number of major hurricanes to strike the US mainland per year was about 0.6. Find the probability that in a given year more than two major hurricanes strike the US mainland.

Answer 1

Answer: A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century, the mean number of major hurricanes to strike the US mainland per year was about 0.6.

Solution:

The probability that in a given year more than two major hurricanes strike the US mainland.

Using Poisson distribution:

P(X = x) = e^-λ * λ^x / x!

Mean, λ = 0.62

P(X > 2) = 1 - P(X ≤ 2)

P(X > 2) = 1 - (P(X = 0) + P(X = 1) + P(X = 2))

P(X > 2) = 1 - [e^-0.6 * 0.6^0 / 0! + e^-0.6 * 0.6^1 / 1! + e^-0.6* 0.6^2 / 2!]

P(X > 2) = 1 - (0.54880 + 0.32929 + 0.09879)

P(X > 2) = 1 - 0.97688

P(X > 2) = 0.02312

Therefore, the probability that in a given year more than two major hurricanes strike the US mainland is 0.02312.