2. Practice
A research was interested in the relation between stress and humor. Below are data from 8 subjects who completed tests of these two traits. Are these two variables related to each other? How much stress would a person probably experience if they had no sense of humor (i.e., score = 0)? How about if they had a high level of humor (i.e., score = 15)?
Stress                Sense of Humor                         4                             2                       10                             8                       12                           11                         5                             3                         7                             8                         6                             7                         2                             3                       14                           13

3. Practice r = .91 Y = .77 + .98(Humor) .77 = .77 + .98(0)
15.47 = (15)
You don’t want to have a sense of humor

7. What is the probability of picking an ace?

8. Probability =

9. What is the probability of picking an ace?
4 / 52 = or 7.7 chances in 100

10. Every card has the same probability of being picked

11. What is the probability of getting a 10, J, Q, or K?

12. (.077) + (.077) + (.077) + (.077) = .308
16 / 52 = .308

13. What is the probability of getting a 2 and then after replacing the card getting a 3 ?

14. (.077) * (.077) = .0059

15. What is the probability that the two cards you draw will be a black jack?

16. 10 Card = (.077) + (.077) + (.077) + (.077) = .308
Ace after one card is removed = 4/51 = .078
(.308)*(.078) = .024

17. Practice
What is the probability of rolling a “1” using a six sided dice?
What is the probability of rolling either a “1” or a “2” with a six sided dice?
What is the probability of rolling two “1’s” using two six sided dice?

18. Practice
What is the probability of rolling a “1” using a six sided dice?
1 / 6 = .166
What is the probability of rolling either a “1” or a “2” with a six sided dice?
What is the probability of rolling two “1’s” using two six sided dice?

19. Practice
What is the probability of rolling a “1” using a six sided dice?
1 / 6 = .166
What is the probability of rolling either a “1” or a “2” with a six sided dice?
(.166) + (.166) = .332
What is the probability of rolling two “1’s” using two six sided dice?

20. Practice
What is the probability of rolling a “1” using a six sided dice?
1 / 6 = .166
What is the probability of rolling either a “1” or a “2” with a six sided dice?
(.166) + (.166) = .332
What is the probability of rolling two “1’s” using two six sided dice?
(.166)(.166) = .028

21. Next step
Is it possible to apply probabilities to a normal distribution?

22. Theoretical Normal Curve
-3 -2 -1  1 2  3 

23. Theoretical Normal Curve
-3 -2 -1  1 2  3 
Z-scores

24. We can use the theoretical normal distribution to determine the probability of an event. For example, do you know the probability of getting a Z score of 0 or less?
.50
-3 -2 -1  1 2  3 
Z-scores

25. We can use the theoretical normal distribution to determine the probability of an event. For example, you know the probability of getting a Z score of 0 or less.
.50
-3 -2 -1  1 2  3 
Z-scores

26. With the theoretical normal distribution we know the probabilities associated with every z score! The probability of getting a score between a 0 and a 1 is
.3413
.3413
.1587
.1587
-3 -2 -1  1 2  3 
Z-scores

27. What is the probability of getting a score of 1 or higher?
.3413
.3413
.1587
.1587
-3 -2 -1  1 2  3 
Z-scores

28. These values are given in Table C on page 400
.3413
.3413
.1587
.1587
-3 -2 -1  1 2  3 
Z-scores

29. To use this table look for the Z score in column A Column B is the area between that score and the mean
Column B
.3413
.3413
.1587
.1587
-3 -2 -1  1 2  3 
Z-scores

30. To use this table look for the Z score in column A Column C is the area beyond the Z score
.3413
.3413
.1587
.1587
-3 -2 -1  1 2  3 
Z-scores

31. The curve is symmetrical -- so the answer for a positive Z score is the same for a negative Z score
Column B
Column C
.3413
.3413
.1587
.1587
-3 -2 -1  1 2  3 
Z-scores

32. Practice
What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
Between mean and z = .56?
Beyond z = 2.25?
Between the mean and z = -1.45

33. Practice
What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
Between mean and z = .56?
.2123
Beyond z = 2.25?
Between the mean and z = -1.45

34. Practice
What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
Between mean and z = .56?
.2123
Beyond z = 2.25?
.0122
Between the mean and z = -1.45

35. Practice
What proportion of the normal distribution is found in the following areas (hint: draw out the answer)?
Between mean and z = .56?
.2123
Beyond z = 2.25?
.0122
Between the mean and z = -1.45
.4265

36. Practice
What proportion of this class would have received an A on the last test if I gave A’s to anyone with a z score of 1.25 or higher?
.1056

38. Note This is using a hypothetical distribution
Due to chance, empirical distributions are not always identical to theoretical distributions
If you sampled an infinite number of times they would be equal!
The theoretical curve represents the “best estimate” of how the events would actually occur

39. Theoretical Distribution

40. Empirical Distribution based on 52 draws

41. Empirical Distribution based on 52 draws

42. Empirical Distribution based on 52 draws

43. Theoretical Normal Curve

44. Empirical Distribution

45. Empirical Distribution

46. Empirical Distribution

47. PROGRAM

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

50. Practice
#7.7
#7.8
#7.9

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

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

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

55. 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!

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

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

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

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

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

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

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

63. 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?

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

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

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

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

68. 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?

69. 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