2. Practice Page 128 –#6.7 –#6.8

3. Practice Page 128 –#6.7 =.0668 = test scores are normally distributed –#6.8 a =.0832 b =.2912 c =.4778

5. Theoretical Normal Curve  Normality frequently occurs in many situations of psychology, and other sciences

6. Putting it together Remember that many empirical distributions are approximately normal

7. Putting it together Thus you can compute z scores from raw scores and use the theoretical normal distribution (Table C) to estimate the probability of that score!

8. Remember Remember how to convert raw scores to Z scores

9. Z-score Z scores have a mean of 0 Z scores have a standard deviation of 1

10. Example: IQ Mean IQ = 100 Standard deviation = 15 What proportion of people have an IQ of 120 or higher?

11. Step 1: Sketch out question -3  -2  -1   1  2  3 

12. Step 1: Sketch out question -3  -2  -1   1  2  3  120

13. Step 2: Calculate Z score -3  -2  -1   1  2  3  120 (120 - 100) / 15 = 1.33

14. Step 3: Look up Z score in Table -3  -2  -1   1  2  3  120 Z = 1.33; Column C =.0918.0918

15. Example: IQ A proportion of.0918 or 9.18 percent of the population have an IQ above 120. What proportion of the population have an IQ below 80?

16. Step 1: Sketch out question -3  -2  -1   1  2  3 

17. Step 1: Sketch out question -3  -2  -1   1  2  3  80

18. Step 2: Calculate Z score -3  -2  -1   1  2  3  80 (80 - 100) / 15 = -1.33

19. Step 3: Look up Z score in Table -3  -2  -1   1  2  3  80 Z = -1.33; Column C =.0918.0918

20. Example: IQ A proportion of.0918 or 9.18 percent of the population have an IQ below 80. In a class with 600 children how many probably have an IQ below 80?

21. Example: IQ A proportion of.0918 or 9.18 percent of the population have an IQ below 80. In a class with 600 children how many probably have an IQ below 80? (.0918) * 600 = 55.08 or 55 children

22. Practice The Neuroticism Measure = 23.32 S = 6.24 n = 54 If your neuroticism score was 36 how many people are likely more neurotic than you in this room?

23. Step 1: Sketch out question -3  -2  -1   1  2  3 

24. Step 2: Calculate Z score -3  -2  -1   1  2  3  (36 - 23.32) / 6.24 = 2.03

25. Step 3: Look up Z score in Table -3  -2  -1   1  2  3  Z = 2.03; Column C =.0212

26. Practice A proportion of.0212 or 2.12 percent of the population is more neurotic. In a class with 54 people 1.14 or 1person is probably more neurotic (.0212) * 54 = 1.14 or 1 person

27. Example: IQ Mean IQ = 100 SD = 15 What proportion of the population have an IQ below 110?

28. Step 1: Sketch out question -3  -2  -1   1  2  3 

29. Step 1: Sketch out question -3  -2  -1   1  2  3  110

30. Step 2: Calculate Z score -3  -2  -1   1  2  3  (110 - 100) / 15 =.67 110

31. Step 3: Look up Z score in Table -3  -2  -1   1  2  3  Z =.67 ; Column B =.2486 110.2486

32. Step 3: Look up Z score in Table -3  -2  -1   1  2  3 .2486 +.50 =.7486 110.2486.50

33. Example: IQ A proportion of.7486 or 74.86 percent of the population have an IQ below 110. In a class with 600 children how many probably have an IQ below 110? (.7486) * 600 = 449.16 or 449 children

34. Practice Mean IQ = 100 SD = 15 What is the probability of randomly selecting someone with an IQ over 80?

35. Step 1: Sketch out question -3  -2  -1   1  2  3 

36. Step 1: Sketch out question -3  -2  -1   1  2  3  80

37. Step 2: Calculate Z score -3  -2  -1   1  2  3  (80 - 100) / 15 = -1.33 80

38. Step 3: Look up Z score in Table -3  -2  -1   1  2  3  Z = -1.33; Column B =.4082 80.4082

39. Step 3: Look up Z score in Table -3  -2  -1   1  2  3 .4082 +.50 =.9082 80.4082.50

40. Example: IQ The probability of randomly selecting someone with an IQ over 80 is.9082

41. Finding the Proportion of the Population Between Two Scores What proportion of the population have IQ scores between 90 and 110?

42. Step 1: Sketch out question -3  -2  -1   1  2  3  11090 ?

43. Step 2: Calculate Z scores for both values Z = (X -  ) /  Z = (90 - 100) / 15 = -.67 Z = (110 - 100) / 15 =.67

44. Step 3: Look in Table C -3  -2  -1   1  2  3 .67-.67.2486

45. Step 4: Add together the two values -3  -2  -1   1  2  3 .67-.67.4972

46. A proportion of.4972 or 49.72 percent of the population have an IQ between 90 and 110.

47. What proportion of the population have an IQ between 110 and 130?

48. Step 1: Sketch out question -3  -2  -1   1  2  3  110130 ?

49. Step 2: Calculate Z scores for both values Z = (X -  ) /  Z = (110 - 100) / 15 =.67 Z = (130 - 100) / 15 = 2.0

50. Step 3: Look in Table C -3  -2  -1   1  2  3 .672.0.4772

51. Step 3: Look in Table C -3  -2  -1   1  2  3 .672.0.4772.2486

52. Step 4: Subtract -3  -2  -1   1  2  3 .672.0.2286.4772 -.2486 =.2286

53. A proportion of.2286 or 22.86 percent of the population have an IQ between 110 and 130.

55. Practice Interpret the following: 1) The correlation between vocational-interest scores at age 20 and at age 40 was.70. 2) Age and IQ is correlated -.16. 3) The correlation between IQ and family size is -.30. 4) The correlation between sexual promiscuity and dominance is.32. 5) In a sample of males happiness and height is correlated.11.