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Homework Help: Probability (Poisson)

  1. Dec 16, 2009 #1
    A machine on average produces 4 defective items out of a batch of 100 items.
    Find the probability that a batch of 50 items has 3 defective items in it using the Poisson probability distribution.

    the problem is..
    i just want to know the mean or average value for batch of 50 items..
    i got mean = 2
    because for 100 items, the mean is 4..
    ............for 50 items, the mean would be 2..
    correct?
     
  2. jcsd
  3. Dec 17, 2009 #2

    Mark44

    Staff: Mentor

    Here's how I would start it. Let the random variable X be the number of defective items in a batch of 50. P(X = 1) = 0.04.

    Assuming that X is Poisson with mean lambda,
    [tex]P(X = k)~= ~\frac{\lambda^k~e^{-k}}{k!}[/tex]
    We also have P(X = 1) = 0.04, so using the equation above, I get
    [tex]\frac{\lambda^1~e^{-\lambda}}{1}~=~0.04[/tex]

    This isn't an equation that you can solve analytically, but you can use estimation techniques to get approximate values for lambda. In about a minute I got a value for lambda of about 4.8. The better you estimate for lambda is, the better your calculation for P(X = 3) will be.
     
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