Question about poisson and probability/exponential distribution

Question

I'm a little confused about this question I was given:

"Calls arrive at a tech support center with a mean of 4 per hour. Assuming the number of calls received in 1hr is described by a Poisson distribution, find the probability that there is more than 20 min between the arrivals of randomly selected successive calls.

λ = 4, but since it is exponential, it is 1/4. The formula I think I need is \int_0^w \lambda e^{-\lambda t} dt

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but I cant figure out what my w should be.

Sorry, I can't figure out how to edit the formula, but its the one in the only answer to this question: https://math.stackexchange.com/questions/235154/probability-question-poisson-and-pmf — Dog with a stick, Nov 14 '19 at 06:39

Michael Hoppe · Answer 1 · 2019-11-14T07:07:26.557

0

Call $X=\text{number of calls per twenty minutes}$. That $X$ is Poisson-distributed with $\lambda=4/3$. Compute $P(X=0)$.

edited Nov 14 '19 at 07:07

answered Nov 14 '19 at 06:47

Michael Hoppe

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when I plug that into the formula -e^-λx, I dont get the right answer – Dog with a stick Nov 14 '19 at 07:01

Question about poisson and probability/exponential distribution

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