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Math Help - Probability that sample mean is greater/less than... (CLT, discrete uniform dist)

  1. #1
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    Probability that sample mean is greater/less than... (CLT, discrete uniform dist)

    Hey mathhelpforum! I'm stuck on a rather simple exercise from Applied statistics and probabilities for engineers, 4th edi.

    it is exercise 7.9. the solution is supposed to be 0,2312.

    Probability that sample mean is greater/less than... (CLT, discrete uniform dist)-win_20140812_163617.jpg

    I try to use the formula Z = (Sample mean - mean) / ((standard deviation)*n^(1/2)),

    so for the first limit, X>2.1, I get (2.1 - 2)/((1/108)^(1/2)). It gives a Z-value of 1.04.
    with sample mean 2.5, the Z-value is waaaaaaay to high.

    What is wrong here? Where is everything falling apart?

    Also, first post, so please correct me if there's something off about the presentation of the question.
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  2. #2
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    Re: Probability that sample mean is greater/less than... (CLT, discrete uniform dist)

    Hey flegmatikern.

    To go through the exercise, you should probably post your calculations for the standard deviation and the mean by evaluating the appropriate integrals for your uniform distribution.

    Chances are if you have an error in these calculations, these will permeate into the Z-statistic. Recall for a continuous distribution: E[X] = Integral[-infinity,infinity) x*f(x)dx.
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  3. #3
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    Re: Probability that sample mean is greater/less than... (CLT, discrete uniform dist)

    Hey! Thanks. There were a few minor issues with my calculations, but it's solved now. Thank you!
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