Answer to Question #191074 in Civil and Environmental Engineering for Joshua

Question

An observer counts 360 vehicles per hour at a highway. Estimate the probability of having more than 4 vehicles arriving over a 25 second time interval.

Answer 1

Solution:

$\lambda=$ 360 vehicles per hour$=0.1$ vehicles per second$=2.5$ vehicles per 25-second

$X\sim Poi(\lambda)$

$P(X\ge4)=1-P(X<4) \\=1-[P(X=0)+P(X=1)+P(X=2)+P(X=3)]$

$=1-[e^{-2.5}\dfrac{(2.5)^0}{0!}+e^{-2.5}\dfrac{(2.5)^1}{1!}+e^{-2.5}\dfrac{(2.5)^2}{2!}+e^{-2.5}\dfrac{(2.5)^3}{3!}]$

$=0.24242$