6-2 Real Applications of Normal Distributions 267 Finding x Values>Areas Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Probability Distributions from the dropdown menu and select Normal Distribution from the submenu. 3. Enter the desired z value or cumulative area from the left of the z score and click Evaluate. TIP: Statdisk does not work directly with nonstandard normal distributions, so use corresponding z scores. StatCrunch 1. Click Stat in the top menu. 2. Select Calculators from the dropdown menu and Normal from the submenu. 3. In the calculator box enter the mean and standard deviation. 4. Enter the desired x value (middle box) or probability (rightmost box). 5. Click Compute. Minitab 1. Click Calc in the top menu. 2. Select Probability Distributions from the dropdown menu and select Normal from the submenu. Finding Cumulative Area to the Left of an x Value 3. Select Cumulative probability, enter the mean and standard deviation. 4. Select Input constant, enter the desired x value, and click OK. Finding x Value from a Known Probability 3. Select Inverse cumulative probability, enter the mean and standard deviation. 4. Select Input constant, enter the total area to the left of the x value, and click OK. TI-83, 84 Plus Calculator Unlike most other technologies, the TI-83>84 Plus bases areas on the region between two z scores, rather than cumulative regions from the left. Finding Area Between Two x Values 1. Press F then O keys to access the DISTR (distributions) menu. 2. Select normalcdf and press [. 3. Enter the desired lower x value and upper x value. Enter the mean 1m2 and standard deviation 1s2 to complete the command normalcdf(lower x,upper x, M, S). Press [. TIP: If there is no lower x value, enter -99999999; if there is no upper x value, enter 99999999. Finding x Value Corresponding to a Known Area 1. Press F then O keys to access the DISTR (distributions) menu. 2. Select invNorm and press [. 3. Enter the area to the left or right of the x value, enter the mean 1m2, and the standard deviation 1s2. For Tail select the tail where the area is located (Left or Right) relative to the x value. The completed command is InvNorm(area, M, S,TAIL). Press [. TIP: The TI-83 Plus only calculates area to the left of the x score. The completed command isInvNorm(area, M, S). R R command not available at time of publication. R is rapidly evolving, and an updated list of statistical commands is available at TriolaStats.com Excel Finding Cumulative Area to the Left of an x Value 1. Click Insert Functionƒx, select the category Statistical, select the function NORM.DIST, and click OK. 2. For x enter the x value, enter Mean, enter Standard_dev, and enter 1 for Cumulative. 3. Click OK. Finding x Value Corresponding to a Known Probability 1. Click Insert Functionƒx, select the category Statistical, select the function NORM.INV, and click OK. 2. Enter the probability or the area to the left of the desired x value, enter Mean, and enter Standard_dev. 3. Click OK.
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