Question #347657

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.

1
Expert's answer
2022-06-03T13:10:12-0400

(a)


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

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

=e6(6)00!+e6(6)11!+e6(6)22!=\dfrac{e^{-6}(6)^0}{0!}+\dfrac{e^{-6}(6)^1}{1!}+\dfrac{e^{-6}(6)^2}{2!}

+e6(6)33!=0.151204+\dfrac{e^{-6}(6)^3}{3!}=0.151204

(b)


P(6X8)=P(X=6)+P(X=7)P(6\le X\le 8)=P(X=6)+P(X=7)

+P(X=8)=e6(6)66!+e6(6)77!+e6(6)88!+P(X=8)=\dfrac{e^{-6}(6)^6}{6!}+\dfrac{e^{-6}(6)^7}{7!}+\dfrac{e^{-6}(6)^8}{8!}

=0.401558=0.401558


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