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    It is claimed that 95% of people in a certain village are right handed. A random sample of 80 villagers are tested to see if they are right or left handed. Use a Poisson approximation to estimate that the number of people that are right handed is:

    a) 80
    b) 79
    c) at least 78

    So I know at first this is a binomial question... n = 80  p = 0.95

    Im going to use z instead of lambda because I Dont know how to make a lambda on the computer :P So  X~Po(z)

    z = mean = np

    so np = z

    z = 0.95 x 80 = 76

     X~Po(76)

     P(X=x) = e^{-z} \times \frac{z^x}{x!}

    So  P(X=80) = e^{-76} \times \frac{76^{80}}{80!} And I got a math error (because the numbers are too small for the calculator i presume)

    I know its probably easier to use a binomial distribution as n is large but p is not small...but the question says use poisson =/

    Where have I gone wrong? Or is the book stupid? :P

    Thanks all
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    The only thing I can think of is doing 1 - the probabilities but for left handed so  n = 0.05
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    Ok ive jsut tried doing 1-left handed and 80! is a math error...so could you do leflt handed for  P(X=80) = 1 - P(X=0) ?
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    Ok just worked it out...work out P(X=0) for left handed people = P(X=80) right handed

    *slap on forehead*
 
 
 
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