Chapter main points

• The normal distribution is central to the theory of inferential statistics. It also provides a model for many empirical distributions that approximate normality.
• In all normal or nearly normal curves, we find a constant proportion of the area under the curve lying between the mean and any given distance from the mean when measured in standard deviation units.
• The standard normal distribution is a normal distribution represented in standard scores, or Z scores, with mean = 0 and standard deviation = 1. Z scores express the number of standard deviations that a given score is located above or below the mean. The proportions corresponding to any Z score or its fraction are organized into a special table called the standard normal table.

Learning objectives

1. Explain the importance and use of the normal distribution in statistics
2. Describe the properties of the normal distribution
3. Transform a raw score into standard (Z) score and vice versa
4. Transform a Z score into proportion (or percentage) and vice versa
5. Calculate and interpret the percentile rank of a score