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Math Help - 1st year probability distribution question

  1. #1
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    1st year probability distribution question

    Hey,

    I was stuck on this question, and have no idea how to go on about solving this. If some one can guide me in this question, it would be really appreciated.

    Aeroplanes arrive at an airport at the average of 5.5 per minute. Traffic controllers can safely handle a maximum of 7 planes per min. What is the probability that airport is safety is jepordised? Planes arrive randomly and independently.

    Thanks
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  2. #2
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    Hello,
    Quote Originally Posted by Subhash View Post
    Hey,

    I was stuck on this question, and have no idea how to go on about solving this. If some one can guide me in this question, it would be really appreciated.

    Aeroplanes arrive at an airport at the average of 5.5 per minute. Traffic controllers can safely handle a maximum of 7 planes per min. What is the probability that airport is safety is jepordised? Planes arrive randomly and independently.

    Thanks
    Isn't it a Poisson distribution ?
    In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate and independently of the time since the last event.
    Poisson distribution - Wikipedia, the free encyclopedia

    X : number of planes
    X \leadsto \mathcal{P}(\lambda), with \lambda=5.5
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  3. #3
    Newbie drichie's Avatar
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    Quote Originally Posted by Subhash View Post
    Hey,

    I was stuck on this question, and have no idea how to go on about solving this. If some one can guide me in this question, it would be really appreciated.

    Aeroplanes arrive at an airport at the average of 5.5 per minute. Traffic controllers can safely handle a maximum of 7 planes per min. What is the probability that airport is safety is jepordised? Planes arrive randomly and independently.

    Thanks
    I think so.

    I am assuming the inter-arrival time follows exponential distribution.ie I am assuming the number of planes arrive per minute follows poisson with mean (lamda) = 5.5

    So. probability that airport is safety is jepordised
    = P[X>8] = 1 - P[X<=7]
    = 1- { exp(-5.5) ( 1 + 5.5/1 + 5.5^2/2! +5.5^3/3! +5.5^4/4! +5.5^5/5! +5.5^6/6! +5.5^7/7! )}

    = 1- 0.8094853
    =0.19
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