Section 7.6 Assessing Normality 337 a straight line when plotted against the xi. Therefore, if the population is approximately normal, it is likely that the points (xi, zi) will approximately follow a straight line. 2 4 6 8 10 2 1 0 −1 −2 z x Figure 7.44 The points do not deviate substantially from a straight line. We can treat this population as approximately normal. Figure 7.45 In practice, normal quantile plots are always constructed with technology. Figure 7.45 presents the normal quantile plot in Figure 7.44 as drawn by the TI-84 Plus calculator. The calculator does not add a line to the plot. Step-by-step instructions for constructing normal quantile plots with the TI-84 Plus calculator are presented in the Using Technology section on page 338. EXAMPLE 7.36 Using a normal quantile plot to assess normality A placement exam is given to each entering freshman at a large university. A simple random sample of 20 exam scores is drawn, with the following results. 61 60 60 68 63 63 94 66 65 98 61 71 74 63 66 61 61 65 72 85 Construct a normal probability plot. Is the distribution of exam scores approximately normal? Solution We use the TI-84 Plus calculator. The results are shown in Figure 7.46. The points do not closely follow a straight line. The distribution is not approximately normal. Figure 7.46 Check Your Understanding 5. Is it reasonable to treat the sample in the following normal quantile plot as coming from an approximately normal population? Explain. Yes 0 5 10 15 3 2 1 0 −1 −2 −3
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