Respuesta :
Solution:
Note that a Poisson probability distribution would be a good choice for r = number of earthquakes in a given time interval. That is, because, the frequency of earthquakes is a rare occurrence. It is reasonable to assume the events are independent.
(a) Compute the probability of at least one major earthquake in the next 51 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)
The average earthquake for the next 51 years is:
[tex]\lambda=\frac{1.5}{22}\text{ x 51}[/tex]that is:
[tex]\lambda=3.477\approx3.48[/tex]now, the probability of at least one major earthquake is given by the following equation:
[tex]P(X\ge1)=1-P(X=0)[/tex]to solve this equation, note that:
[tex]P(X=0)=\frac{e^{-3.48}.3.48^0}{0!}=0.0308[/tex]thus,
[tex]P(X\ge1)=1-P(X=0)=\text{ 1-0.03080=0.969}2[/tex]then, the correct answer is:
[tex]\text{0.969}2[/tex](b) Compute the probability of no major earthquakes in the next 51 years. Round to the nearest hundredth, and use a calculator. (Use 4 decimal places.)
The probability of no major earthquakes in the next 51 years is given by P(X=0).
P(X=0) is calculated in the above item which is:
[tex]P(X=0)=\frac{e^{-3.48}.3.48^0}{0!}=0.0308[/tex]so that, the correct answer is:
[tex]0.0308[/tex]
