340 Chapter 7 The Normal Distribution 3 2 1 0 −1 −2 −3 −10 0 10 20 30 40 x z Working with the Concepts 19. Drug concentrations: A sample of 10 people ingested a new formulation of a drug. Six hours later, the concentrations in their bloodstreams, in nanograms per milliliter, were as follows. 2.3 1.4 1.8 2.1 1.0 4.1 1.8 2.9 2.5 2.7 Construct a dotplot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. No 20. Reading scores: A random sample of eight elementary school children were given a standardized reading test. Following are their scores. 72 77 65 85 68 83 73 79 Construct a dotplot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. Yes 21. Timed task: The number of minutes needed to complete a certain spreadsheet task was measured for 20 clerical workers. The results were as follows. 4.5 5.8 3.7 4.9 4.3 4.7 5.8 3.2 3.0 5.1 3.6 4.3 3.6 5.4 4.7 3.0 3.4 4.3 4.4 3.5 Construct a boxplot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. Yes 22. Impure cans: A manufacturer of aluminum cans measured the level of impurities in 24 cans. The amounts of impurities, in percent, were as follows. 2.1 1.5 1.9 1.3 2.7 4.9 2.1 1.8 1.3 1.0 3.2 4.4 8.0 4.5 2.5 1.6 2.8 8.2 9.5 3.8 1.9 1.5 2.8 1.6 Construct a boxplot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. No 23. Defective items: The number of defective items produced on an assembly line during an hour is counted for a random sample of 20 hours. The results are as follows. 21 16 10 10 11 9 13 12 11 29 10 14 27 10 11 11 12 19 11 9 Construct a stem-and-leaf plot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. No 24. Fish weights: A fish hatchery raises trout to stock streams and lakes. The weights, in ounces, of a sample of 18 trout at their time of release are as follows. 9.9 11.3 11.4 9.0 10.1 8.2 8.9 9.9 10.5 8.6 7.8 10.8 8.4 9.6 9.9 8.4 9.0 9.1 Construct a stem-and-leaf plot for this sample. Is it reasonable to treat the sample as coming from an approximately normal population? Explain. Yes 25. Timed task: Construct a histogram for the data in Exercise 21. Explain how the histogram shows whether it is appropriate to treat this sample as coming from an approximately normal population. Approximately normal 26. Impure cans: Construct a histogram for the data in Exercise 22. Explain how the histogram shows whether it is appropriate to treat this sample as coming from an approximately normal population. Not normal 27. Defective items: Construct a normal quantile plot for the data in Exercise 23. Explain how the plot shows whether it is appropriate to treat this sample as coming from an approximately normal population. Not normal 28. Fish weights: Construct a normal quantile plot for the data in Exercise 24. Explain how the plot shows whether it is appropriate to treat this sample as coming from an approximately normal population. Approximately normal Extending the Concepts 29. Transformation to normality: Consider the following data set: 2 37 67 108 148 40 1 9 3 237 12 80 a. Show that this data set does not come from an approximately normal population. b. Take the square root of each value in the data set. This is called a square-root transformation of the data. Show that the square roots may be considered to be a sample from an approximately normal population. 30. Transformation to normality: Consider the following data set: −0.5 0.8 1.7 −1.0 −10.0 1.7 0.5 0.3 −5.0 a. Show that this data set does not come from an approximately normal population. b. Take the reciprocal of each value in the data set (the reciprocal of x is 1∕x). This is called a reciprocal transformation of the data. Show that the reciprocals may be considered to be a sample from an approximately normal population. 31. Transformation to normality: Consider the following data set: 4.1 2.7 1.2 10.3 0.9 2.4 1.5 1.9 2.1 16.1 1.4 1.0 a. Is it reasonable to treat it as a sample from an approximately normal population? No b. Perform a square-root transformation. Is it reasonable to treat the square-root-transformed data as a sample from an approximately normal population? No c. Perform a reciprocal transformation. Is it reasonable to treat the reciprocal-transformed data as a sample from an approximately normal population? Yes
navidi_monk_elementary_statistics_2e_ch7-9
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