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Math Help - Probability Question (Help Please)

  1. #1
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    Probability Question (Help Please)

    Hey i need help on this question, after reading the book it doesn't give any helpful advice on how to solve this problem, or how to do it.

    When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck to not meet the desired standard. What's the probability that the shipment will be accepted anyways?
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  2. #2
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    Quote Originally Posted by KyKy View Post
    Hey i need help on this question, after reading the book it doesn't give any helpful advice on how to solve this problem, or how to do it.

    When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck to not meet the desired standard. What's the probability that the shipment will be accepted anyways?

    5%*150 = 7.5 defects.

    Let X be a binomial random variable; the number of defective apples found.

    Use a binomial distribution with p=8% and compute
    P(shipment\;will\; not\; be\; rejected) =P(X\leq{7}) = \sum_{k=0}^{7}\binom{150}{k}(.08)^k(.92)^{150-k}
    Last edited by vince; February 19th 2010 at 02:10 PM. Reason: substituted n=150 in the formula
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  3. #3
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    one thing that's bugging me about using a binomial here is that once we find a defective apple, the remaining number of defective apples in the shipment is lessened -- we're not replacing the defective apples to keep the proportion the same throughout the trials. i think im wrong actually, but close. let me now consider poisson.
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  4. #4
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    nah...since these are independent trials, the realization of a defective apple doesnt propagate to affect the probabaility of the next trial's outcome. i think it's fine as is. i get the prob is ~8%. poisson would work here too since 150*.08 isn't large...
    Last edited by vince; February 19th 2010 at 02:53 PM. Reason: corrected the probablility...
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