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Let $X$ be the number of cars per minute passing a certain point on Sunday from 8AM to 10AM. Assume that $X$ has poisson distribution with mean $5$. Find the probability observing $4$ or fewer car in any given minute?

Here is what I got. Since this is a poisson distribution with mean $5$

$P$(4 cars or fewer)$=f(0)+f(1)+f(2)+f(3)+f(4)$

$=e^{-5}(\frac{5^0}{0!}+\frac{5^1}{1!}+\frac{5^2}{2!}+\frac{5^3}{3!}+\frac{5^4}{4!})$ $=44.05$%

but the book says it's $26.5$%. Did I misunderstand the question somehow?

Diane Vanderwaif
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1 Answers1

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Your answer looks right to me. If you work out the probability that (strictly) fewer than $4$ cars are observed it comes to $26.5$%. If you are sure you have quoted the question correctly, then maybe the authors had a brain fade when they wrote the answer section ;-)

David
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