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I have this question, which I keep getting the incorrect answer to.

The number of planes arriving per day at a small private airport is a random variable having a Poisson distribution with γ = 28.8. What is the probability that the time between two such arrivals is atleast one hour.

The book says the answer is .1827, but I have no clue how they came to this answer. I have the formula

P(x; λ )= $ λ^x$ $e^{- λ}$ / x!

x = events in the interval , λ = average number of events per interval

But I must be plugging the incorrect values in. There were also examples on using exponential distribution with poissons, and I'm not sure if this is this case.

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  • $\begingroup$ Can you describe what the formula means? (for example, what is $x$?) What numbers have you tried "plugging in"? Show us what you have tried and what was your thinking behind it. $\endgroup$ – Thanassis Nov 14 '16 at 1:22
  • $\begingroup$ First, check your formula. Second, the arrival rate per hour is $28.8/24$ assuming a constant rate and 24hr a day operation. Third, if you are implying an answer in a book may be wrong, you have an obligation so give author, title, year and publisher--and to say what you think is correct. $\endgroup$ – BruceET Nov 14 '16 at 1:35
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The book answer is wrong, it happens, especially with new edition books..

Interval time can be represented with an exponential distribution. But Bruce gave you a nice hint of using 28.8/24 (which equals 1.2) as your parameter for arrival times per hour.

The necessary probability is equal to the probability that there will be NO arrivals in an hour. Since, the arrivals per hour follow a poisson distribution just use Lambda = 1.2 and x = 0 and plug into your poisson function. You'll see the answer will come out to e^-1.2, which is about 30%

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