Chapter Main Points and Learning Objectives
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.
- Explain the importance and use of the normal distribution in statistics
- Describe the properties of the normal distribution
- Transform a raw score into standard (Z) score and vice versa
- Transform a Z score into proportion (or percentage) and vice versa
- Calculate and interpret the percentile rank of a score