2. Practice
#7.7
#7.8
#7.9

3. Practice 7.7 7.8 7.9 .0668 Normal distribution
A = .0832; B = .2912; C = .4778
7.9
Empirical

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

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

6. 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!

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

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

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

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

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

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

13. Step 3: Look up Z score in Table
Z = 1.33; Column C = .0918
120
.0918
-3 -2 -1  1 2  3 

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

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

16. Step 1: Sketch out question80
-3 -2 -1  1 2  3 

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

18. Step 3: Look up Z score in Table
Z = -1.33; Column C = .0918 80
.0918
-3 -2 -1  1 2  3 

19. Example: IQ
A proportion of 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?

20. Example: IQ
A proportion of 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 = or 55 children

21. 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?

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

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

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

25. Practice
A proportion of 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

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

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

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

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

30. Step 3: Look up Z score in Table
Z = .67 ; Column B = .2486
110
.2486
-3 -2 -1  1 2  3 

31. Step 3: Look up Z score in Table
= .7486
110
.50
.2486
-3 -2 -1  1 2  3 

32. Example: IQ
A proportion of or 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 = or 449 children

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

34. Step 1: Sketch out question
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35. Step 1: Sketch out question80
-3 -2 -1  1 2  3 

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

37. Step 3: Look up Z score in Table
Z = -1.33; Column B = .4082 80
.4082
-3 -2 -1  1 2  3 

38. Step 3: Look up Z score in Table
= .9082 80
.4082
.50
-3 -2 -1  1 2  3 

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

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

41. Step 1: Sketch out question90
110 ?
-3 -2 -1  1 2  3 

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

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

44. Step 4: Add together the two values
-.67
.67
.4972
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45. A proportion of .4972 or 49.72 percent of the population have an IQ between 90 and 110.

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

47. Step 1: Sketch out question
110
130 ?
-3 -2 -1  1 2  3 

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

49. Step 3: Look in Table C
.67
2.0
.4772
-3 -2 -1  1 2  3 

50. Step 3: Look in Table C
.67
2.0
.4772
.2486
-3 -2 -1  1 2  3 

51. Step 4: Subtract
= .2286
.67
2.0
.2286
-3 -2 -1  1 2  3 

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

53. Practice The Neuroticism Measure = 23.32 S = 6.24 n = 54
How many people likely have a neuroticism score between 29 and 34?

54. Practice (29-23.32) /6.24 = .91 B = .3186 ( 34-23.32)/6.26 = 1.71
= .1378
.1378*54 = 7.44 or 7 people

56. Finding a score when given a probability
What IQ score is required to fall in the top 20 percent of the population?

57. Step 1: Sketch out question
.20 ?

58. Step 2: Look in Table C
In column C get as close to .20 as you can and find the corresponding Z score = .84
.20 ?

59. Step 3: Find the X score that goes with the Z score
Z = (X -  ) / 
.84 = (X - 100) / 15
Must solve for X
X =  + (z)()
X = (.84)(15)

60. Step 3: Find the X score that goes with the Z score
Z = (X -  ) / 
.84 = (X - 100) / 15
Must solve for X
X =  + (z)()
X = (.84)(15) = 112.6
A score of is needed to be in the top 20 percent!

62. 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.