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Math Help - Mean of sample(help)

  1. #1
    Yan
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    Mean of sample(help)

    Independent random samples of size n1=30 and n2=50 are taken from two normal populations having the means μ1=78 and μ2=75 and the variances σ21=150 and σ22=200. Find the probability that the mean of the first sample will exceed that of the second sample by at least 4.8.
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    Flow Master
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    Quote Originally Posted by Yan View Post
    Independent random samples of size n1=30 and n2=50 are taken from two normal populations having the means μ1=78 and μ2=75 and the variances σ21=150 and σ22=200. Find the probability that the mean of the first sample will exceed that of the second sample by at least 4.8.
    Sample mean is a normally distributed random variable. And the difference of two normally distributed random variables is also a normally distributed random variable.

    So find \Pr(Y > 4.8) where Y = \overline{X}_1 - \overline{X}_2.

    Researching the details is left for you to do.
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