Question #191074

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.

Expert's answer

**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)\n\\\\=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"

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