Monday
May 25, 2015

Homework Help: Statistics (Poisson)

Posted by Sean on Sunday, July 19, 2009 at 4:46pm.

Cars arrive at a toll booth according to a Poisson process with mean 80 cars per hour.

How long can the attendant's phone call last if the probability is at least .4 that no cars arrive during the call.

The book's answer is 23 seconds. That doesn't match mine and I was hoping to understand why...

p(y) = λ^y * e^-λ / y!
p(0) = e^-λ

p(0) > 0.4
e^-λ > 0.4
-λ > ln 0.4
λ < -ln 0.4

If x = call length (in seconds)
λ = x * 80 / 3600

x * 80/3600 < -ln 0.4
x < -3600/80 * ln 0.4
x < 41.2 seconds

Can anyone point out how to get 23 seconds or what I did wrong?

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