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Math Help - X~N(mu,sigma) Probability Averages

  1. #1
    Pur
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    X~N(mu,sigma) Probability Averages

    Assume X~ N(\mu,\sigma). If we take a random sample of size n, how do we calculate that the probability of the average of the sample is at least \mu+c \quad \forall{C}\in{\mathbb{R}}. ie
    P(X_1+X_2+\cdots+X_n \geq n\cdot (\mu+C))
    Last edited by Pur; February 7th 2009 at 09:22 AM.
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  2. #2
    Flow Master
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    Quote Originally Posted by Pur View Post
    Assume X~ N(\mu,\sigma). If we take a random sample of size n, how do we calculate that the probability of the average of the sample is at least \mu+c \quad \forall{C}\in{\mathbb{R}}. ie
    P(X_1+X_2+\cdots+X_n \geq n\cdot (\mu+C))
    Use the sampling distribution of the mean (see Sampling distribution - Wikipedia, the free encyclopedia)
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  3. #3
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    As directed by Pur, sampling distibution of normals is another normal with mean=mu and std=sigma/sqrt(n).

    -O
    Last edited by mr fantastic; February 7th 2009 at 08:04 PM. Reason: Removed link not relevant to question (looks like a signature but isn't)
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