334 Chapter 7 The Normal Distribution EXAMPLE 7.33 Use a histogram to assess normality Recall: Histograms were introduced in Section 2.2. Diameters were measured, in millimeters, for a simple random sample of 20 grade A eggs from a certain farm. The results were 59 60 60 56 59 56 62 58 60 59 61 59 61 61 63 60 56 58 63 58 Construct a histogram for these data. Is it reasonable to treat this as a sample from an approximately normal population? Explain. Solution Figure 7.41 presents a relative frequency histogram of the diameters. The histogram does not reveal any outliers, nor does it exhibit a large degree of skewness. 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. 56 57 58 59 60 61 62 63 0.20 0.15 0.10 0.05 0 Relative Frequency Diameter (millimeters) Figure 7.41 The histogram of the egg diameters does not reveal any outliers, nor a large degree of skewness, nor evidence of more than one mode. Therefore, we can treat this as a sample from an approximately normal population. EXAMPLE 7.34 Use a histogram to assess normality A shoe manufacturer is testing a new type of leather sole. A simple random sample of 22 people wore shoes with the new sole for a period of four months. The amount of wear on the right shoe was measured for each person. The results, in thousandths of an inch, were 24.1 2.2 11.8 2.7 4.1 13.9 33.6 2.4 36.2 16.8 5.4 4.6 4.5 4.1 6.1 6.3 22.6 29.1 12.2 4.6 15.8 7.7 Construct a histogram for these data. Is it reasonable to treat this as a sample from an approximately normal population? Explain. Solution Figure 7.42 presents a relative frequency histogram of the amounts of wear. The histogram reveals that the sample is strongly skewed to the right. We should not treat this as a sample from an approximately normal population. 2 6 10 14 18 22 26 30 34 38 0.4 0.3 0.2 0.1 0 Relative Frequency Wear (thousandths of an inch) Figure 7.42 The histogram is strongly skewed. Therefore, we should not treat this as a sample from an approximately normal population.
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