APPENDIX C Normal Probability Plots A29 MINITAB Score Player heights Normal Probability Plot of Player Heights Normal 2 1 0 –1 –2 65 70 75 80 85 90 Constructing a normal probability plot by hand can be rather tedious. You can use technology such as Minitab, Excel, StatCrunch, or the TI-84 Plus to construct a normal probability plot, as shown in Example 1. Constructing a Normal Probability Plot The heights (in inches) of 12 randomly selected current National Basketball Association players are listed. Use technology to construct a normal probability plot to determine whether the data come from a population that has a normal distribution. (Source: NBA Media Ventures, LLC) 74 70 78 75 73 71 80 82 81 76 86 77 SOLUTION Using Minitab, enter the heights into column C1. From the Graph menu, select “Probability Plot,” choose the option “Single,” and click OK. Next, select column C1 as the graph variable. Then click “Distribution” and choose “Normal” from the drop-down menu. Click the Data Display tab, select “Symbols only,” and click OK. After clicking “Scale,” click the Y-Scale Type tab, select “Score,” and click OK. Click OK to construct the normal probability plot. Your result should be similar to the one shown below. (To construct a normal probability plot using a TI-84 Plus, follow the instructions in the Tech Tip at the left.) MINITAB Score Player heights Normal Probability Plot of Player Heights Normal 2 1 0 –1 –2 70.0 72.5 75.0 77.5 80.0 82.5 85.0 87.5 Interpretation Because the points are approximately linear, you can conclude that the sample data come from a population that has a normal distribution. TRY IT YOURSELF 1 The balances (in dollars) on student loans for 18 randomly selected college seniors are listed. Use technology to construct a normal probability plot to determine whether the data come from a population that has a normal distribution. 29,150 16,980 12,470 19,235 15,875 8,960 16,105 14,575 39,860 20,170 9,710 19,650 21,590 8,200 18,100 25,530 9,285 10,075 Answer: Page A43 To see that the points are approximately linear, you can graph the regression line for the observed values from the data set and their expected z-scores. The regression line for the heights and expected z-scores from Example 1 is shown in the graph at the left. From the graph, you can see that the points lie along the regression line. You can also approximate the mean of the data set by determining where the line crosses the x-axis. EXAMPLE 1 Tech Tip Here are instructions for constructing a normal probability plot using a TI-84 Plus. First, enter the data into List 1. Then use Stat Plot to construct the normal probability plot, as shown below. Plot1 Plot2 Plot3 On Type: Data List:L1 Off Data Axis:X Y Mark: 65 90 3 −3
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