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Math Help - Probability for binomial distribution

  1. #1
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    Probability for binomial distribution

    Hey all you binomial distribution fanatics out there!

    My question is:
    Let x be a binomial random variable and suppose n= 20, p=0.2. Then P(μ-σ ≤ x ≤ μ+σ) is:
    The following is my attempt:
    I know that:
    μ = n*p = 20*0.2 = 4
    σ = sqrt(npq) = 1.788

    So Im looking for the the range of x being between 2.21 and 5.788
    But the binomial distribution chart for n = 20 only shows k values for whole numbers, so what I would be looking for is: (k=5)-(k=3), which is 0.804-0.411=0.393
    However the correct answer is 0.844

    can someone help me solve this?
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  2. #2
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    Re: Probability for binomial distribution

    Quote Originally Posted by snypeshow View Post
    Hey all you binomial distribution fanatics out there!
    However the correct answer is 0.844
    \sum\limits_{k = 2}^6 {{\binom{20}{k}{\left( {0.2} \right)}^k}{{\left( {0.8} \right)}^{20 - k}}}  = {\text{0}}{\text{.84413219615619}}
    That gives you the given answer.
    I suppose they rounded \sigma=2.

    On this link scroll down to normal approximations.
    That may help with this.
    Last edited by Plato; March 7th 2012 at 02:29 PM.
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    Re: Probability for binomial distribution

    Quote Originally Posted by Plato View Post
    \sum\limits_{k = 2}^6 {{\binom{20}{k}{\left( {0.2} \right)}^k}{{\left( {0.8} \right)}^{20 - k}}}  = {\text{0}}{\text{.84413219615619}}
    That gives you the given answer.
    I suppose they rounded \sigma=2.
    Thanks so much for helping me with this!

    I do have a few questions about what you did (to help further my understanding):

    In this part: \sum\limits_{k = 2}^6 did you round 2.21 down to 2 and 5.78 up to 6? (just to confirm, this part means the sum of the probabilities when X is between 2 and 6 right?)

    or are those numbers totally different? and how would \sigma=2 affect the question, since you aren't using it?
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    Re: Probability for binomial distribution

    Quote Originally Posted by snypeshow View Post
    In this part: \sum\limits_{k = 2}^6 did you round 2.21 down to 2 and 5.78 up to 6? (just to confirm, this part means the sum of the probabilities when X is between 2 and 6 right?)
    or are those numbers totally different? and how would \sigma=2 affect the question, since you aren't using it?
    Go to my edited post. Follow that link. I think that will help.
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    Re: Probability for binomial distribution

    ah, ok! That's perfect, thanks so much (again)!!
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