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Math Help - Question regarding the normal approximation to the binomial probablility distribution

  1. #1
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    Unhappy Question regarding the normal approximation to the binomial probablility distribution

    Hello, I am really having trouble with this one:

    Q.
    Data collected over a long period of time show that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x=60 children with the defect in a total of 50,000 examined. If the 50,000 were a random sample from the population of children represented by past records,What is the probability of observing a value of X eqaul to 60 or more?

    Any help will be greatly appreciated,
    Cheers, RaVS
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by RaVS View Post
    Hello, I am really having trouble with this one:

    Q. Data collected over a long period of time show that a particular genetic defect occurs in 1 of every 1000 children. The records of a medical clinic show x=60 children with the defect in a total of 50,000 examined. If the 50,000 were a random sample from the population of children represented by past records,What is the probability of observing a value of X eqaul to 60 or more?

    Any help will be greatly appreciated,
    Cheers, RaVS
    Assume the normal approximation is valid then the expected number with the defect is 50 and its SD is \sqrt{50000(1-1/1000)/1000} \approx \sqrt{50}

    CB
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  3. #3
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    Thank you Captain Black, your help is greatly appreciated.
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  4. #4
    MHF Contributor matheagle's Avatar
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    with n large and p REALLY small I would think that the Poisson limit is correct and not the normal.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by matheagle View Post
    with n large and p REALLY small I would think that the Poisson limit is correct and not the normal.
    The condition that I use when considering the normal approximation is \mu \gg \sigma. In practice this means that \sqrt{Np} \gg 1

    Depending on the time of day and wind direction this can mean anything from \mu \ge 3 \sigma to \mu \ge 10 \sigma, or if we are discussing very low probability events \mu \ge 100 \sigma to never (low probability events that occur in certain safety analyses for example).

    Actually that is not what I usually do; I always first consider the normal approximation and only if the answer using that is not blindingly clear do I resort to exact calculation (or a better approximate method), that and the desire to impress simple minds. Reality does not really support high precision probability calculations, but we don't tell the punters this.


    CB
    Last edited by CaptainBlack; April 28th 2010 at 01:45 AM.
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