Question

Assume that the Poisson distribution applies and that the mean number of hurricanes in a certain area is 5.8 per year. a. Find the probability​ that, in a​ year, there will be 3 hurricanes. b. In a 45​-year ​period, how many years are expected to have 3 ​hurricanes? c. How does the result from part​ (b) compare to a recent period of 45 years in which 4 years had 3 ​hurricanes? Does the Poisson distribution work well​ here?

Answer 1

Answer:

a. 0.098

b. 4.41

c. Yes, it does.

Step-by-step explanation:

a.

The Poisson distribution's equation is:

P(x) = (nˣ*e⁻ⁿ)/x!

where P is the probability, n is mean number, and x the number of the event happens, so:

$P(3) = \frac{5.8^3*e^{-5.8}}{3!}$

P(3) = 0.098

b.

For 45 years, the years that are expected to have 3 hurricanes are

P(3) * 45 = 0.098*45 = 4.41

c.

Yes, it does. The Poisson distribution works well because the observed value of the number of years that 3 hurricanes occur is 45-year period is very close to the calculated value.