of 1) is called the standard normal distribution, which represents a distribution of z-scores. Standard Normal Distributions and Z ScoresĪ normal distribution that is standardized (so that it has a mean of 0 and a S.D. This fact, as described in the Central Limit Theorem, is critical for many applications of statistical inference. Although a distribution of scores in a sample of N cases may be quite far from normal, the distribution of means for all possible samples of N cases may be quite close to normal. Important note: Before we use the normal distribution to compute probabilities, we must verify that the distribution of interest is very close to normal. The normal distribution may characterize either distributions of individual data points in a population of scores or the theoretical distribution of sample statistics such as the mean. The total area under the curve sums to 100%. Tails of a normal distribution are asymptotic, indefinitely decreasing but never touching the x-axis. Although normal distributions may have different means and standard deviations, all normal distributions are “bell-curve” shaped, symmetrical with the greatest height at the mean. The normal distribution is defined by a mathematical formula.
