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Standard Normal Random Variable
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\(Z = \frac{(X - \mu)}{\sigma}\)

  • \(Z\) - standard normal random variable
  • \(X\) - normal random variable
  • \(\mu\) - mean of X
  • \(\sigma\) - standard deviation of X

Every normal distribution can be transformed into the standard normal distribution.

For a standard normal random variable: mean = 0 and standard deviation = 1.

In the cumulative distribution function tables for the standard normal distribution we can find probabilities that are true also for the corresponding not-standardized normal random variable.