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Math Help - poisson distribution

  1. #1
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    poisson distribution

    The number of batteries sold per week by a garage may be assumed to have a poisson distribution with mean 5.

    a) Find the probability that

    i)exactly 6 are sold in a randomly chosen week
    ii) exactly 6 are sold in each of 3 randomly chosen weeks
    iii) exactly 18 are sold in a randomly chosen 3-week period.

    b) Find, approximately, the probability that more than 240 are sold in a randomly chosen 52-week period.

    OK firstly i write

    X~Po(5)

    for a-i i get this

    P(X=6) = \frac{e^-5 * 5^6}{6!} = 0.1462

    is this agreed?

    for part a-ii i'm not sure whether to simply do (0.1462)^3

    or rewrite X~Po(15) ...?

    part a-iii presents the same problem.

    for part b i try

    X~Po(5*52) = X~Po(260)

    P(x>240) = 1 - P(x<240)

    Z = \frac{X-\mu}{\sigma} = \frac{240-260}{\surd{260}} = -0.39

    \phi(-0.39) = 0.34827

    but i'm not sure :/
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  2. #2
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    Quote Originally Posted by djmccabie View Post
    The number of batteries sold per week by a garage may be assumed to have a poisson distribution with mean 5.

    a) Find the probability that

    i)exactly 6 are sold in a randomly chosen week
    ii) exactly 6 are sold in each of 3 randomly chosen weeks
    iii) exactly 18 are sold in a randomly chosen 3-week period.

    b) Find, approximately, the probability that more than 240 are sold in a randomly chosen 52-week period.

    OK firstly i write

    X~Po(5)

    for a-i i get this

    P(X=6) = \frac{e^-5 * 5^6}{6!} = 0.1462

    is this agreed?

    for part a-ii i'm not sure whether to simply do (0.1462)^3 Right

    or rewrite X~Po(15) ...? No, then you would be ignoring the "in each of 3 weeks" part of the problem and just looking at the total number.

    part a-iii presents the same problem.

    for part b i try

    X~Po(5*52) = X~Po(260)

    P(x>240) = 1 - P(x<240)

    Z = \frac{X-\mu}{\sigma} = \frac{240-260}{\surd{260}} = -0.39

    \phi(-0.39) = 0.34827

    but i'm not sure :/ The approach is right but your arithmetic is wrong.
    See above.
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  3. #3
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    ahaa i mean \phi (-1.24)

    is that correct?

    for part a then would i write X~Po(15)?



    appreciate the help!
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  4. #4
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    Quote Originally Posted by djmccabie View Post
    ahaa i mean \phi (-1.24)

    is that correct?

    for part a then would i write X~Po(15)?



    appreciate the help!
    For part a-iii you can use a Poisson distribution with mean 15, yes.
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