Question

Suppose that during a recent 25​-year ​period, there were four volcanic eruptions sufficiently powerful to reduce the amount of power generated by solar panels by at least 20​% for a period of a year. Call these​ "ClassD20​" volcanoes. Suppose that the return on investment from installing solar panels is often calculated over a 15​-year period. What is the probability​ that, during a 15​-year ​period, there will be two or more​ "ClassD20​" volcanic​ eruptions?

Answer 1

The rate of the ClassD20 volcanoes in 25 years is 4

So the rate of the ClassD20 volcanoes in 15 years is = 15*(4/25) =3*(4/5) =12/5 = 2.4 =

Let X = the number of ClassD20 volcanoes in 15 years

So X takes values as 0, 1, 2, ...

Therefore X follows Poisson distribution with parameter = 2.4

What is the probability​ that, during a 15​-year​period, there will be two or more​ "ClassD20​" volcanic​eruptions?

mathematically, P(X >= 2) = 1 - P(X <= 1) = 1 - P(X =0) - P(X = 1) ...( 1 )

The formula of Poisson distribution is

x = 0, 1, 2, 3, ....

For = 2.4 , we get

This is the final answer.