Measures of reading ability, introversion, job satisfaction, and memory are among the many psychological variables approximately normally distributed. Although the distributions are only approximately normal, they are usually quite close. A second reason the normal distribution is so important is that it is easy for mathematical statisticians to work with. This means that many kinds of statistical tests can be derived for normal distributions. Fortunately, these tests work very well even if the distribution is only approximately normally distributed.
Some tests work well even with very wide deviations from normality.
Finally, if the mean and standard deviation of a normal distribution are known, it is easy to convert back and forth from raw scores to percentiles . Converting between scores from a normal distribution and percentile ranks. If the mean and standard deviation of a normal distribution are known, it is relatively easy to figure out the percentile rank of a person obtaining a specific score. Example 1 Assume a test in Introductory Psychology is normally distributed with a mean of 80 and a standard deviation of 5. Mathematical statisticians have developed ways of determining the proportion of a distribution that is below a given number of standard deviations from the mean.