# Poisson Distribution with time.

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.

• 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. – Thanassis Nov 14 '16 at 1:22
• 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. – BruceET Nov 14 '16 at 1:35