Question

A certain area of the eastern United States is, on average, hit by 6 hurricanes a year. Find the probability 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) fewer than 4 hurricanes;

$P(X)=\frac{\lambda^{X}e^{-\lambda}}{X!}$

$P(X<4)=P(X=0)+P(X=1)+P(X=2)+P(X=3)$

$=\frac{6^{0}e^{-6}}{0!}+\frac{6^{1}e^{-6}}{1!}+\frac{6^{2}e^{-6}}{2!}+\frac{6^{3}e^{-6}}{3!}$

$=0.0025+0.0149+0.0446+0.0892$

$=0.1512$

(b) anywhere from 6 to 8 hurricanes;

$P(X)=\frac{\lambda^{X}e^{-\lambda}}{X!}$

$P(6\eqslantless X\eqslantless8)=P(X=6)+P(X=7)+P(X=8)$

$=\frac{6^{6}e^{-6}}{6!}+\frac{6^{7}e^{-6}}{7!}+\frac{6^{8}e^{-6}}{8!}$

$=0.1606+0.1376+0.1033$

$=0.4015$