Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.5 per year.

a.) Find the probability that in a year, there will be 3 hurricanes.

Answer 1

The probability of there being exactly 3 hurricanes in a year can be calculated using the Poisson distribution formula, this value can be calculated as approximately 0.135.

Step-by-step explanation:

The subject of this question is Mathematics, specifically dealing with the Poisson distribution, which is a probability distribution that measures the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

To calculate the probability of exactly 3 hurricanes in a year, we can use the Poisson distribution formula. The formula is P(x; λ) = (e^-λ * λ^x) / x!, where λ is the mean number of hurricanes in the given area. In this case, λ = 5.5. Plugging in x = 3 and λ = 5.5, we get:

P(3; 5.5) = (e^-5.5 * 5.5^3) / 3!

Using a calculator, this value can be calculated as approximately 0.135.