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Math Help - Probability question

  1. #1
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    Probability question

    Q: A company purchases shipments of machine components and uses this acceptance sampling plan: Randomly select and test 24 components and accept the whole batch if there are fewer than 3 defectives. If a particular shipment of thousands of components actually has a 4% rate of defects, what is the probability that this whole shipment will be accepted?

    A: 0.9307

    I'm not sure how to set up the equation to solve it. Any help is appreciated.
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  2. #2
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    Use the binomial theorem

    P(X=k) = \binom{n}{k}p^k(1-p)^{n-k}

    where n = 24, p= 96/100 (96% = 1 - 4%), k=24 (the entire shipment!)


     P(X=24) = \binom{24}{24}(\tfrac{96}{100})^24(1-\tfrac{96}{100})^{24-24}= \cdots
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  3. #3
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    Sorry but when trying to calculate the above I can't seem to get the answer of 0.9307
    Not sure why that is...
    Also, how did you get k=24 if the problem says that the shipment is "thousands"?
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  4. #4
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    Oops sorry! I prorbably read the question a little too quick! Let me re-think...
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  5. #5
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    It's okay, thanks for helping me.

    Edit: Maybe there is a mistake? Since the amount is unknown.
    Last edited by Lovely07; May 19th 2009 at 05:39 AM.
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