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A simple statistic question

  1. May 4, 2009 #1
    1. The problem statement, all variables and given/known data

    how to do with the normal distribution if the mean is not 0 variance is not 1.
    for example p(x>1) if x-N(2,3) ?

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 4, 2009 #2

    Mark44

    Staff: Mentor

    You use a transformation of your random variable X, namely z = (x - mu)/sigma. Here z is N(0, 1).
    The transformation works the other way, too, with x = z sigma + mu.
    The probability you want is
    P(x > 1)
    = P(z sigma + mu > 1)
    Work with the expression in parentheses above, using the properties of inequalities, to get a probability involving z all by itself. The idea is that if you have equivalent inequalities, the probabilities will be equal. You should end up with a probability of the form P(z > ...). You can find that probability in a table of standard normal distribution probabilities.
     
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