A28 APPENDIX C What You Should Learn How to construct and interpret a normal probability plot Normal Probability Plots For many of the examples and exercises in this text, it has been assumed that a random sample is selected from a population that has a normal distribution. After selecting a random sample from a population with an unknown distribution, how can you determine whether the sample was selected from a population that has a normal distribution? You have already learned that a histogram or stem-and-leaf plot can reveal the shape of a distribution and any outliers, clusters, or gaps in a distribution (see Sections 2.1, 2.2, and 2.3). These data displays are useful for assessing large sets of data, but assessing small data sets in this manner can be difficult and unreliable. A reliable method for assessing normality in any data set is to use a normal probability plot. A normal probability plot (also called a normal quantile plot) is a graph that plots each observed value from the data set along with its expected z-score. The observed values are usually plotted along the horizontal axis while the expected z-scores are plotted along the vertical axis. DEFINITION The guidelines below can help you determine whether data come from a population that has a normal distribution. 1. If the plotted points in a normal probability plot are approximately linear, then you can conclude that the data come from a normal distribution. 2. If the plotted points are not approximately linear or follow some type of pattern that is not linear, then you can conclude that the data come from a distribution that is not normal. 3. Multiple outliers or clusters of points indicate a distribution that is not normal. Two normal probability plots are shown below. The normal probability plot on the left is approximately linear. So, you can conclude that the data come from a population that has a normal distribution. The normal probability plot on the right follows a nonlinear pattern. So, you can conclude that the data do not come from a population that has a normal distribution. 0 Expected z-score Observed value y x 40 42 44 46 50 52 54 56 58 −1 −2 −3 1 2 3 0 Expected z-score Observed value y x 46 48 52 54 56 58 60 −1 −2 −3 1 2 3 Normal Probability Plots C
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