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Math Help - Stats/Prop question regarding sample sets

  1. #1
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    Question {solved}Stats/Prop question regarding sample sets

    The problem is:

    A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet the specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

    1) Can anyone put this in dummy terms for me, and

    2) Whats the answer and how did you get it?

    Thanks
    Last edited by tuxedomask419; February 2nd 2009 at 05:43 PM. Reason: solved
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  2. #2
    Junior Member mathhomework's Avatar
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    My Answer

    A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet the specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

    Please check my answer. I am not sure.

    1. sameple space is 100 and 7.3% fails, the failing filters are about 7.3 for every 100 filters.

    2. The probability of having less than 5 failing filters is impossible because we already know that for every 100, at least 7.3 filters fail to meet the specification.

    p(5 or less)=0
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  3. #3
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    Quote Originally Posted by mathhomework View Post
    A machine cuts circular filters from large rolls of material. If 7.3% of the filters fail to meet the specifications, use the normal approximation to the binomial to compute the probability that a sample of 100 of the filters will contain 5 or fewer that fail to meet specifications.

    Please check my answer. I am not sure.

    1. sameple space is 100 and 7.3% fails, the failing filters are about 7.3 for every 100 filters.

    2. The probability of having less than 5 failing filters is impossible because we already know that for every 100, at least 7.3 filters fail to meet the specification.

    p(5 or less)=0
    This is wrong.

    Let X be the random variable Number of filters that fail to meet specifications.

    X ~ Binomial(n = 100, p = 0.073)

    Note: "7.3% of filters fail to meet the specifications" means that p = 0.073.

    You have to calculate Pr(X \leq 5) using the normal approximation to the binomial distribution.

    Now read 5.2 of this: Binomial distribution - Wikipedia, the free encyclopedia
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