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Math Help - normal approximation to the binomial

  1. #1
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    normal approximation to the binomial

    I know this should be easy but I'm not seeing it.

    Question: On average, 3% of the watches manufactured by a particular company will be returned for warranty repair. Use the normal approximation to the binomial to find the probability that among 1000 watches sold, 40 or fewer will be returned.

    I have that 3% of 1000 is 30 which is my mean.
    So, (40-30)/ \sigma=probability

    And I'm stuck here, because I can't see the standard deviation. Once I have that I can get a value that I can look up in the tables, correct?

    Any help would be appreciated.
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  2. #2
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    Re: normal approximation to the binomial

    I can't see the standard deviation
    use the standard deviation of the binomial distribution you are trying to approximate, which is \sqrt{np(1-p)}


    (40-30)/=probability
    I think you mean (40-30)/ = Z
    and you intend to look up the probability associated with the Z value in your tables.

    PS Do you need a continuity correction?
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  3. #3
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    Re: normal approximation to the binomial

    Thank you.

    (40-30)/15.8=.6329 I looked up .6329 and came up with a probability of .7357.
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  4. #4
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    Re: normal approximation to the binomial

    IIRC, you need a continuity correction.
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  5. #5
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    Re: normal approximation to the binomial

    (40.5-30)/15.8=.6646 with Probability = .7454

    Thank you.
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