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Math Help - A coil of wire has 400 metres of wire. Suppose there are 20 nicks.

  1. #1
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    A coil of wire has 400 metres of wire. Suppose there are 20 nicks.

    A coil of wire has 400 metres of wire. Suppose there are 20 nicks (the most common problem with wire) are randomly distributed on a coil.

    What is the probability that in a 40 metre length of wire there will be at least 6 nicks?
    What is the probability that in a 49 metre length of wire there will be exactly 4 nick(s)?

    I know that I have to use the poisson distribution, but I have to do it in excel using
    =POISSON(x,mean,1 or 0), and I have no idea what to do.
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  2. #2
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    If you know there are exactly 20 nicks in the 400 metre coil, then the poisson distribution may be inappropriate. This is because the poisson distribution will give a nonzero probability of finding more than 20 nicks in any segment.

    however if your teacher told you to use the poisson distribution then I would assume that the expected number of nicks per metre is 0.05. (20/400 =0.05).

    The number of nicks (x) in a segment of length (k) is then distributed as \sim Po(0.05k)

    (a)The number of nicks on a segment of length 40 follows a po(0.05*40) = po(2) distribution

    P(x \geq 6) = 1-p(x \leq 5)

    Excel will tell you p(x \leq 5) :
    in excel 2003, this is POISSON(5,2,1)
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