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Math Help - Sample question

  1. #1
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    Sample question

    I have been away from math for a while. I appreciate the help here tremendously.

    the problem: In manufacturing, a sample of 4 items from a lot of 100 is taken.
    The lot is rejected if at least 1 is defective.
    Graph the probability that the lot is accepted as a function of the percentage of defective items in the lot.

    I included an attachment that tries to explain my thought process on the attached problem. I am completely stuck like chuck on the graph also.

    If the attachment doesn't work I saved it to a link also.

    thanks in advance.

    Andy

    http://www.orbitfiles.com/download/id791674014
    Attached Thumbnails Attached Thumbnails Sample question-lot100.jpg  
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  2. #2
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    Quote Originally Posted by andy_atw
    the problem: In manufacturing, a sample of 4 items from a lot of 100 is taken.
    The lot is rejected if at least 1 is defective.
    Graph the probability that the lot is accepted as a function of the percentage of defective items in the lot.
    A lot is accepted if none are defective. So the probability is P(\text{accepted}) = P(4\ \text{not\ de{f}ective}) = (1 - k/100)^4 .
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  3. #3
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    explain

    Jake...I have been pondering the problem for a while now, and I am not grasping the logic in determining the answer. please explain further. thanks
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  4. #4
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    Quote Originally Posted by andy_atw
    Jake...I have been pondering the problem for a while now, and I am not grasping the logic in determining the answer. please explain further. thanks
    Arghh, you're right. Sorry about that. I used a sample with replacement. This should be a sample without replacement.

    So using the hypergeometric distribution the probability of no defectives is \frac{{k \choose 0}{100-k \choose  4}}{{100 \choose 4}} = \frac{{100-k \choose  4}}{{100 \choose 4}}. This is the number of ways of choosing 4 out of 100-k nondefectives over the number of ways of choosing 4 out of 100.
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