Answer to Question #347657 in Statistics and Probability for lojy

Question

A certain area of the eastern United States is, on average, hit by 6 hurricanes a year. Find the prob-ability that in a given year that area will be hit by (a) fewer than 4 hurricanes; (b) anywhere from 6 to 8 hurricanes.

Answer 1

(a)

$$P(X<4)=P(X=0)+P(X=1)$$

$$+P(X=2)+P(X=3)$$

$$=\dfrac{e^{-6}(6)^0}{0!}+\dfrac{e^{-6}(6)^1}{1!}+\dfrac{e^{-6}(6)^2}{2!}$$

$$+\dfrac{e^{-6}(6)^3}{3!}=0.151204$$

(b)

$$P(6\le X\le 8)=P(X=6)+P(X=7)$$

$$+P(X=8)=\dfrac{e^{-6}(6)^6}{6!}+\dfrac{e^{-6}(6)^7}{7!}+\dfrac{e^{-6}(6)^8}{8!}$$

$$=0.401558$$