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15 July, 20:42

The rate of defects among cd players of a certain brand is 1.5%. use the poisson approximation to 19) the binomial distribution to find the probability that among 430 such cd players received by a store, there are exactly three defective cd players.

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  1. 15 July, 21:14
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    The solution for the problem using binomial distribution:

    Given:

    p = 1.5% or 0.015

    n = 430

    Mean = lambda = m = np = 430*0.015 = 6.45 According to Poisson distribution:

    P (x) = e^ - (np) * (np) ^x Where:

    P is the probability of x

    n is the sample size

    e is the exponential constant

    P (3) = e^ - (430*1.5/100) * (430*1.5/100) ^3

    P (3) = 0.00158 * 268.3336125

    P (3) = 0.4240%
  2. 15 July, 22:31
    0
    The poison distribution can be used to approximate the binomial distribution when the sample size n is large. This is then calculated using the formula P (X) = e^ - (np) * (np) ^x substituting X = 3 P (3) = e^ - (430*1.5/100) * (430*1.5/100) ^3 P (3) = 0.00158*268.3 P (3) = 0.42 P (3) = 0.0042% P = probability of X occurring given n and p n = sample size p = true probability e = exponential constant ~2.718 X=number of sample successes
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