1. Psychology 290 – Lab 9 January 23 - 25 Normal Distribution Standardization Z-scores

2. Distributions

3. Z-Score Transformation to calculate a z-score to calculate a raw score

4. E.g. Raw score to z-score #1 Mean = 100; S = 15 Determine percentage of people who scored higher than 110. Z = 110 – 100 = 10 = 0.67 15 15 Next step is to look up 0.67 in the z column in z-table at the back of the book In this case: Mean to z will provide the % between 100 and 110 Larger portion will provide the % below 110 Smaller portion will provide the % above 110

5. E.g. cont. Under the “Smaller Portion” column, the value associated with a z-score of 0.67 is 0.2514. This means that 25.14% of individuals score higher than 110.

6. E.g. Raw score to z-score #2 Mean = 100; S = 15 Determine percentage of scores between 85 and 120. Z = 85 – 100 = -15 = -1 15 15 Z = 120 – 100 = 20 = 1.33 15 15

7. E.g. #2 cont. Use z-table to look up and add values under the Mean to z column. For z = -1; Mean to z = 0.3413 For z = 1.33; Mean to z = 0.4082 Therefore, area between is: 0.3413 + 0.4082 = 0.7495 or 74.95%

8. E.g. z-score to raw score Mean = 100; S = 15 What is the raw score associated with the 63 rd percentile. 63% = 0.63 Look for 0.63 in the z-table under the “Larger Portion” section. (To be conservative, use 0.6293) Associated z-score = 0.33

9. E.g. cont. x = 0.33(15) + 100 x = 4.95 + 100 x = 104.95