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Math Help - a poisson process problem

  1. #1
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    a poisson process problem

    A merchant finds that 20% of customers ask for an item which is not in stock.
    Customers arrive according to the conditions for a Poisson process with an
    average rate of 12 per hour.

    (1) Find the probability of 5 customers arriving in a 10-minute period.
    (2) Find the probability 3 customers ask for an item that is not in stock, out of 20 customers at the store.
    (3) Find the probability the xth customer arriving at the store is the 3rd to ask for an item which is not in stock.
    (4) Give an expression for the probability that 3 customers will ask for an item that is not in stock during a 75-minute period.


    for 1. i think it is f(5) = (2^5*e^-2) / 5!

    for 2. i think it is (20 Choose 3)*(0.2)^3*(0.8)^17

    for 3, i think it is ((x-1)choose 2)* (0.2)^3*(0.8)^(x-3)

    i am not sure how to do 4
    thanks a lot
    Last edited by dull1234; October 28th 2009 at 07:32 PM.
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