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Math Help - Calculating the Expected Cost. Help!

  1. #1
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    Calculating the Expected Cost. Help!

    Hi guys,

    I have been set the following question and I'm really struggling and need some advice. I think I may have completed it, but it seems too simple, so I am just after some confirmation if it's right or not.

    The question is as follows:

    A particular type of electronic component for use in PCs is mass produced and subject to quality control checks since it is known that 4% of all components produced in this way are defective. The quality of a day's output is monitored as follows. A sample of 15 components is drawn from the day's output (which may be assumed to be large) and inspected for defective components. If this sample contains 0 or 1 defectives the day's output is accepted , otherwise it is rejected. If it contains more than 2 defectives the output is rejected. If the sample contains 2 defectives a second sample of 15 is taken. If this sample contains 0 defectives the output is accepted, otherwise it is rejected.

    So far I have worked out the following:

    P(0 defectives) = 0.542
    P(1 defective) = 0.339
    P(2 defectives) = 0.099

    I have then worked out the probably of 2 defectives and then 0 defectives in the second sample is 0.099 x 0.542 = 0.054. However I'm not sure this is correct.

    I have then worked out the probability of the accepted output to be 0.542 + 0.339 + 0.054 = 0.935

    I have then been asked the following:

    Suppose that it is estimated that it costs 100 to inspect a sample of 15. What is the expected cost of a day's sampling?

    I have simply done 100 x 0.935 = 93.50. Cost of daily sampling = 93.50.

    I appreciate any help given on this
    Last edited by mr fantastic; February 13th 2011 at 11:34 AM. Reason: Restored deleted question.
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  2. #2
    Pim
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    If I read the question correctly, your final answer is not correct.

    The probabilities (P(0 defectives), P(1 defective), P(2 defectives)) you calculated are correct, but your follow-up steps seem hinky. It is said that it costs 100 pounds to inspect a sample. You will atleast inspect one sample a day. Hence the expected cost should be at least 100 pounds.

    So the next question is: In which case do you sample more than once in a day?
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  3. #3
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    Thanks for the response. However, I've asked for the thread to be deleted as it is related to some coursework that I am doing, and I was unaware that I couldn't post questions that are related to any academic work. I appreciate your help.
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  4. #4
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    Quote Originally Posted by Gall1987 View Post
    Please can this thread be closed. Thanks
    Why does this tread require deleting? Your duplicate post you also required deleting as well. It makes sense to have one deleted but both? The only possible reason you want that could be that what Pim wrote allowed you to fix your mistake and this is an assignment to be graded so you are detroying the evidence.
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  5. #5
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    Quote Originally Posted by Gall1987 View Post
    Thanks for the response. However, I've asked for the thread to be deleted as it is related to some coursework that I am doing, and I was unaware that I couldn't post questions that are related to any academic work. I appreciate your help.
    If you don't have to turn it in for a grade, you can ask for help.
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  6. #6
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    The work doesn't count towards my overall grade, but it is work that we have to complete for lessons and we get assessed on this. I've asked for them both to be deleted as I thought they infringed the forum's rules.
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