The standard-normal distribution, along with the calculation of z-scores, provides a basis for determining the probabilities of possible outcomes for a continuous variable and also forms the basis for many other distributions that you will come across in your studies. A qualification must be made. Using the standard-normal distribution and z-scores to determine probabilities requires that the population mean and population standard deviation are known.

Any set of scores transformed into z-scores will have a mean of 0.0 and a standard deviation of 1.0. A z-score indicates how many standard deviations the corresponding original score is from the original mean. For example, a z-score of -2.5 indicates that the original score was 2.5 standard deviations below the original mean; a z-score of 1.0 indicates that the original score was 1.0 standard deviation above the mean. Creating z-scores is the first step toward computing the probabilities of possible outcomes from a continuous variable.