A4 APPENDIX A Alternative Presentation of the Standard Normal Distribution You can use the following guidelines to find various types of areas under the standard normal curve. Finding Areas Under the Standard Normal Curve 1. Sketch the standard normal curve and shade the appropriate area under the curve. 2. Use the Standard Normal Table (0-to-z) on page A1 to find the area that corresponds to the z-score(s). 3. Find the area by following the directions for each case shown. a. Area to the left of z i. When z 6 0, subtract the area from 0.5. ii. When z 7 0, add 0.5 to the area. −1.23 z 0 Subtract to find the area to the left of z = −1.23; 0.5 − 0.3907 = 0.1093. 2. The area between z = 0 and z = −1.23 is 0.3907. 1. 1.23 z 0 Add to find the area to the left of z = 1.23; 0.5 + 0.3907 = 0.8907. 2. The area between z = 0 and z = 1.23 is 0.3907. 1. b. Area to the right of z i. When z 6 0, add 0.5 to the area. ii. When z 7 0, subtract the area from 0.5. −1.23 z 0 Add to find the area to the right of z = −1.23; 0.5 + 0.3907 = 0.8907. 2. The area between z = 0 and z = −1.23 is 0.3907. 1. 1.23 z 0 Subtract to find the area to the right of z = 1.23; 0.5 − 0.3907 = 0.1093. The area between z = 0 and z = 1.23 is 0.3907. 1. 2. c. Area between two z-scores i. When the two z-scores have the same sign ii. When the two z-scores have opposite signs (both positive or both negative), subtract (one negative and one positive), add the the smaller area from the larger area. areas. 1.23 z 0 2.5 The area between z = 0 and z2 = 2.5 is 0.4938. Subtract to find the area between z1 = 1.23 and z2 = 2.5; 0.4938 − 0.3907 = 0.1031. 3. 2. The area between z = 0 and z1 = 1.23 is 0.3907. 1. 1.23 z 0 −0.5 The area between z = 0 and z2 = −0.5 is 0.1915. Add to find the area between z1 = 1.23 and z2 = −0.5; 0.3907 + 0.1915 = 0.5822. 3. 2. The area between z = 0 and z1 = 1.23 is 0.3907. 1. GUIDELINES
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