Psychology 290 – Lab 9 January Normal Distribution Standardization Z-scores

Distributions

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

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 = 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

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

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

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 = For z = 1.33; Mean to z = Therefore, area between is: = or 74.95%

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 ) Associated z-score = 0.33

E.g. cont. x = 0.33(15) x = x =