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Math Help - ball carton

  1. #1
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    Question ball carton

    Any help offered in solving the below question will be much appreciated.
    Thanks
    Kingman

    A manufacturer makes balls which are packed in cartons of 20 and send to market
    for sale. A ball will not meet the minimum requirement for packing for sale if it weighs less than 20 grams. On average 2% of the balls made did not meet the minimum requirement.

    Find the probability that out of 4 randomly chosen cartons of balls, there are exactly 2 cartons with at least 1 ball that does not meet the minimum requirement. (0.295)
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  2. #2
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    Well, there are a couple of things that you have to do here.

    First, we must find the probability of at least 1 ball in a carton of 20 weighing less than 20g.

    We can use a binomial distribution for this. Here's the formula.

    pr(X=x)={k\choose x}p^{x}(1-p)^{(k-x)}

    X~binomial(k=20,p=0.02)

    X= the number of balls that weigh less than 20g.

    We're looking for pr(X\geq 1)

    Using the Axioms of Probability this can be rewritten as  1 - pr(X<1) which is the same as 1-pr(X=0)

    Using the binomial distribution formula given above solve

    1-pr(X=0)

    Your answer (I'll call it y) will be used in the second part.

    Now we need to find the probability that out of 4 randomly selected cartons, exactly 2 will have at least 1 ball that does not meet the minimum weight requirement.

    Again, we can use a binomial distribution.

    X~binomial(k=4, p=y)

    X= the number of cartons that have at least 1 ball that does not meet the minimum weight requirement.

    Now simply use the binomial distribution formula to solve

    pr(X=2)=...\approx 0.295
    Last edited by downthesun01; May 20th 2010 at 03:44 AM.
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