Suppose that the number of drivers who travel between aparticular orgin and dest

Question

Suppose that the number of drivers who travel between aparticular orgin and destination during a designated time periodhas a Poisson distribution with parameter = 20. In thelong run, in what proportion of time periods will the number ofdrivers a. Be at most 10? b. Exceed 20? c. Be between 10 and 20, inclusive? Be strictly between 10 and20? Suppose that the number of drivers who travel between aparticular orgin and destination during a designated time periodhas a Poisson distribution with parameter = 20. In thelong run, in what proportion of time periods will the number ofdrivers a. Be at most 10? b. Exceed 20? c. Be between 10 and 20, inclusive? Be strictly between 10 and20?

Explanation / Answer

poission probability distibution functionis p(x=k) = e- k /k!          =20 1) p (x <_ 10) = e-2020k /k!     where k = 1 , 2 ,3 ----------9 , 10 2) p(x .> 20) = 1 - p(x <_ 20)                        = 1 - e-20 20k/k!        k = 1 2 3 ----------19, 20 3) p( 10 <_x < _20) = e-20 20k /k!   k = 10 11 12 13 ------------19 . 20

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