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The Normal distribution is frequntly encountered in real life. Often a matter of interest is how likely it is that the random variable (RV) being studied takes a value that it did or one that is more extreme. This requires a comparison of the observed value of the RV with its Normal distribution. Unfortunately, the general Normal distribution is extremely difficult to calculate.
The Normal distribution is defined by two parameters: the mean and the variance (or standard deviation). It is impossible to tabulate the distribution of every possible combination of two parameters - both of which are continuous real numbers. However, using Z score reduces the problem to that of tabulating only one the Normal distribution: the N(0, 1) or standard Normal distribution. This allows the analysis of an RV with any Normal distribution.
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