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    Normal an Poisson approximation to binomial distribution

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    In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365.

    For a given month find:
    1) The probability taht in a group of 10 bondholders each holding 5000 bonds, four or more win at least one prize,
    2) The probability in a group of 100 bondholders each holding 5000 bonds, 40 or more win at least one prize.
    Find the expected number of prizes for a bondholder holding 550 bonds for 24 months.

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    https://brainmass.com/statistics/probability/normal-poisson-approximation-binomial-distribution-10742

    Solution Preview

    Let X be the number of prizes won.
    X ~ Bin(5000, 1/11000)

    Since n is large, p is very small,
    such that np = 5/11

    We use Poisson approximation to binomial distribution.
    X ~ P(5/11) approx

    P( X >= 1) = 1 - P(X=0)
    = 1 - e^-5/11
    = 0.365 ...

    Solution Summary

    In each month, the proportion of "Prize" bonds that win a prize is 1 in 11000. There is a large number of prizes and all bonds are equally likely to win each prize. Show that, for a given month, the probability that a bondholder with 5000 bonds wins at least one prize is 0.365.

    For a given month find:
    1) The probability taht in a group of 10 bondholders each holding 5000 bonds, four or more win at least one prize,
    2) The probability in a group of 100 bondholders each holding 5000 bonds, 40 or more win at least one prize.
    Find the expected number of prizes for a bondholder holding 550 bonds for 24 months.

    $2.49

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