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Math Help - the normal approximation

  1. #1
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    Question the normal approximation

    A clothing manufacturer estimates from past quality control inspections that 4.8% of sweatshirts produced are irregular. If an inspector randomly selects 650 sweatshirts, estimate the probability that at least 30 are irregular.
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  2. #2
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    Quote Originally Posted by terminator View Post
    A clothing manufacturer estimates from past quality control inspections that 4.8% of sweatshirts produced are irregular. If an inspector randomly selects 650 sweatshirts, estimate the probability that at least 30 are irregular.
    Where are you stuck in applying the normal approximation to the binomial distribution? Please show some effort.
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  3. #3
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    np = 350x0.10 = 35
    n(1-p) =350 x 0.90 = =315

    np>=5, n(1-p) >=5
    Therefore, the approximation is resonably close to a normal distribution because
    np <= 5 and n(1-p) >=5
    Now I can calculate the standard deviation
    mean = np =35
    sd= sqr(npq) =5.61
    How do I calculate the probability?


    "In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
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  4. #4
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    Quote Originally Posted by terminator View Post
    np = 350x0.10 = 35
    n(1-p) =350 x 0.90 = =315

    np>=5, n(1-p) >=5
    Therefore, the approximation is resonably close to a normal distribution because
    np <= 5 and n(1-p) >=5
    Now I can calculate the standard deviation
    mean = np =35
    sd= sqr(npq) =5.61
    How do I calculate the probability?


    "In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
    http://courses.wcupa.edu/rbove/Beren...section6_5.pdf
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  5. #5
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    Thanks mr.Fantastic - you're a nice man
    "In mathematics, you don't understand things. You just get used to them." -- Johann von Neumann
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