when you doesnt have information about the real mean of a population and use the estimation of mean instead of the real mean , usually you use t distribution instead of normal distribution.
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Intersting but nothing to do with the question!
If a random variable X is distributed Normally with mean m and standard deviation s, then Z = (X-m)/s has a standard Normal distribution.
Z has mean 0 and standard deviation = 1 (or Variance = sd2 = 1).
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