332 Chapter 7 The Normal Distribution SUMMARY We will reject the assumption that a population is approximately normal if a sample has any of the following features: 1. The sample contains an outlier. 2. The sample exhibits a large degree of skewness. 3. The sample is multimodal; in other words, it has more than one distinct mode. If the sample has none of the preceding features, we will treat the population as being approximately normal. Many methods have been developed for assessing normality; some of them are quite sophisticated. For our purposes, it will be sufficient to examine dotplots, boxplots, stemand leaf plots, and histograms of the sample. We will also describe normal quantile plots, which provide another useful method of assessment. Objective 1 Use dotplots to assess normality Dotplots Dotplots are excellent for detecting outliers and multimodality. They can also be used to detect skewness, although they are not quite as effective as histograms for that purpose. EXAMPLE 7.29 Using a dotplot to assess normality Recall: Dotplots were introduced in Section 2.3. The accuracy of an oven thermostat is being tested. The oven is set to 360◦F, and the temperature when the thermostat turns off is recorded. A sample of size 7 yields the following results: 358 363 361 355 367 352 368 Is it reasonable to treat this as a sample from an approximately normal population? Explain. Solution Figure 7.37 presents a dotplot of the temperatures. The dotplot does not reveal any outliers. The plot does not exhibit a large degree of skewness, and there is no evidence that the population has more than one mode. Therefore, we can treat this as a sample from an approximately normal population. 350 355 360 365 370 Figure 7.37 The dotplot of the oven temperatures does not reveal any outliers. The plot does not exhibit a large degree of skewness, and there is no evidence that the population has more than one mode. Therefore, we can treat this as a sample from an approximately normal population. EXAMPLE 7.30 Using a dotplot to assess normality At a recent health fair, several hundred people had their pulse rates measured. A simple random sample of six records was drawn, and the pulse rates, in beats per minute, were 68 71 79 98 67 75 Is it reasonable to treat this as a sample from an approximately normal population? Explain. Solution Figure 7.38 presents a dotplot of the pulse rates. It is clear that the value 98 is an outlier. Therefore, we should not treat this as a sample from an approximately normal population. 65 70 75 80 85 90 95 100 Figure 7.38 The value 98 is an outlier. Therefore, we should not treat this as a sample from an approximately normal population.
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