6-1 The Standard Normal Distribution 257 Finding z Scores>Areas (Standard Normal) 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 score or cumulative area from the left of the z score and click Evaluate. 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 mean of 0 and standard deviation of 1. 4. Enter the desired z score (middle box) or known probability> area (rightmost box). Select the desired inequality. 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 a z Score • Select Cumulative probability, enter mean of 0 and standard deviation of 1. • Select Input Constant, enter the desired z score, and click OK. Finding z Score from a Known Probability • Select Inverse cumulative probability, enter mean of 0 and standard deviation of 1. • Select Input Constant, enter the total area to the left of the z score, 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 z Scores 1. Press F then O keys to access the DISTR (distributions) menu. 2. Select normalcdf and press [. 3. Enter the desired lower z score and upper z score. Enter 0 for m and 1 for s to complete the command normalcdf(lower z,upper z,M,S). Press [. TIP: If there is no lower z score, enter -99999999; if there is no upper z score, enter 99999999. Finding z Score from a Known Probability 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 z score, 0 for m, and 1 for s. For Tail select the tail where the area is located (Left or Right). The completed command is InvNorm(area,0,1,TAIL). Press [. TIP: The TI-83 Plus only calculates area to the left of the z score. The completed command is InvNorm(area,0,1). 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 a z Score 1. Click Insert Functionƒx, select the category Statistical, select the function NORM.DIST, and click OK. 2. For x enter the z score, enter 0 for Mean, enter 1 for Standard_dev, and enter 1 for Cumulative. 3. Click OK. Finding z Score from a Known Probability 1. Click Insert Functionƒx, select the category Statistical, and select the function NORM.INV. 2. Enter the probability, enter 0 for Mean, and enter 1 for Standard_dev. 3. Click OK.
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