1. Approximating distributions
Binomial distribution
Approximating distributions
Normal distribution
Poisson distribution
Approximating distributions: Nannestad

2. Approximating distributions: Nannestad
Binomial to Normal
Binomial distribution
Normal distribution
Poisson distribution
Approximating distributions: Nannestad

3. Approximating the binomial distribution with a normal distribution
has discrete data
and looks like
Normal
has continuous data
and looks like f
0.15
0.1
0.05 x 2 4 6 8 10 12
Approximating distributions: Nannestad

4. Approximating distributions: Nannestad
Why bother?
Tables are not readily available for large values of n.
When n is large, and p is not too close to either 0 or 1, then the binomial values are reasonably symmetrical.
In these conditions, the normal curve closely fits the binomial values.
Approximating distributions: Nannestad

5. Approximating distributions: Nannestad
How do we approximate a binomial distribution with a normal distribution?
The mean of a binomial distribution with n terms and probability p is np,
and the variance is np(1-p).
Use these values as the mean and variance for a normal distribution.
Approximating distributions: Nannestad

6. When is the normal approximation “good enough”?
Look at the following examples.
When is the normal curve “close enough” to the binomial distribution?
Approximating distributions: Nannestad

7. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.10
Normal: mean = 1.50, VAR = 1.35 f
Binomial: n = 15, p = 0.10
0.3
Normal: mean = 1.50, VAR = 1.35
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

8. Approximating distributions: Nannestad
Binomial: n = 15, p = 0. 15
Normal: mean = 2.25, VAR = 1.91 f
Binomial: n = 15, p = 0.15
0.3
Normal: mean = 2.25, VAR = 1.91
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

9. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.20
Normal: mean = 3.00, VAR = 2.40 f
Binomial: n = 15, p = 0.20
0.3
Normal: mean = 3.00, VAR = 2.40
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

10. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.25
Normal: mean = 3.75, VAR = 2.81 f
Binomial: n = 15, p = 0.25
0.3
Normal: mean = 3.75, VAR = 2.81
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

11. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.30
Normal: mean = 4.50, VAR = 3.15 f
Binomial: n = 15, p = 0.30
0.3
Normal: mean = 4.50, VAR = 3.15
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

12. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.35
Normal: mean = 5.25, VAR = 3.41 f
Binomial: n = 15, p = 0.35
0.3
Normal: mean = 5.25, VAR = 3.41
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

13. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.40
Normal: mean = 6.00, VAR = 3.60 f
Binomial: n = 15, p = 0.40
0.3
Normal: mean = 6.00, VAR = 3.60
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

14. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.45
Normal: mean = 6.75, VAR = 3.71 f
Binomial: n = 15, p = 0.45
0.3
Normal: mean = 6.75, VAR = 3.71
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

15. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.50
Normal: mean = 7.50, VAR = 3.75 f
Binomial: n = 15, p = 0.50
0.3
Normal: mean = 7.50, VAR = 3.75
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

16. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.55
Normal: mean = 8.25, VAR = 3.71 f
Binomial: n = 15, p = 0.55
0.3
Normal: mean = 8.25, VAR = 3.71
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

17. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.60
Normal: mean = 9.00, VAR = 3.60 f
Binomial: n = 15, p = 0.60
0.3
Normal: mean = 9.00, VAR = 3.60
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

18. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.65
Normal: mean = 9.75, VAR = 3.41 f
Binomial: n = 15, p = 0.65
0.3
Normal: mean = 9.75, VAR = 3.41
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

19. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.70
Normal: mean = 10.5, VAR = 3.15 f
Binomial: n = 15, p = 0.70
0.3
Normal: mean = 10.5, VAR = 3.15
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

20. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.75
Normal: mean = 11.3, VAR = 2.81 f
Binomial: n = 15, p = 0.75
0.3
Normal: mean = 11.3, VAR = 2.81
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

21. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.80
Normal: mean = 12.0, VAR = 2.40 f
Binomial: n = 15, p = 0.80
0.3
Normal: mean = 12.0, VAR = 2.40
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

22. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.85
Normal: mean = 12.8, VAR = 1.91 f
Binomial: n = 15, p = 0.85
0.3
Normal: mean = 12.8, VAR = 1.91
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

23. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.90
Normal: mean = 13.5, VAR = 1.35 f
Binomial: n = 15, p = 0.90
0.3
Normal: mean = 13.5, VAR = 1.35
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

24. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.95
Normal: mean = 14.3, VAR = 0.71 f
Binomial: n = 15, p = 0.95
0.3
Normal: mean = 14.3, VAR = 0.71
0.2
0.1 x 5 10 15 20
Approximating distributions: Nannestad

25. Approximating distributions: Nannestad
General guidelines
We can approximate the binomial distribution with n terms and probability p with the corresponding normal distribution when both
np5, and
n(1-p)5.
Approximating distributions: Nannestad

26. Approximating distributions: Nannestad
For the example with n = 15 and p changes by 0.05 each time, this would require p values 0.35  p  0.65
Approximating distributions: Nannestad

27. What happens to the values when we change from discrete data to continuous data?
In a binomial distribution we can have a probability for a single value.
Example: For binomial n = 15, p = 0.40,
P(X=4) =
However, it is not possible to have proability for a single value in normal distribution.
Example: Normal: mean = 6.00, VAR = 3.60,
P(X=4) cannot exist.
Why?
Approximating distributions: Nannestad

28. The probability is calculated from the area under the normal curve.
For the area to be other than zero we need to find the probability between two values
Approximating distributions: Nannestad

29. Continuity correction
When approximating a discrete distribution with one that is continuous we must apply a continuity correction.
Original binomial distribution
n = 30, p = 0.7
   
The value for P(X = 20) in the binomial distribution
Approximating distributions: Nannestad

30. Approximating distributions: Nannestad
Binomial to Normal
Binomial distribution
Normal distribution
Poisson distribution
Approximating distributions: Nannestad

31. Approximating distributions: Nannestad
Binomial to Poisson
Binomial distribution
Normal distribution
Poisson distribution
Approximating distributions: Nannestad

32. Approximating distributions: Nannestad
When the binomial value for n is large and p is very small
the event is considered “rare”
and we can approximate values with the Poisson distribution.
Approximating distributions: Nannestad

33. Approximating the binomial distribution with a poisson distribution
has discrete data
and looks like
Poisson
has disctrete data
and looks like f
0.3
0.2
0.1 x
Approximating distributions: Nannestad 2 4 6 8 10

34. Approximating distributions: Nannestad
When? Why? How?
When the value of p is too small for the tables, the probability of the event occuring is becoming “rare”. (np < 5 is a fair guide.)
Binomial tables do not give the required values.
Using np = , the binomial distribution values are approximated by the Poisson distribution.
Approximating distributions: Nannestad

35. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.005
Poisson:  = 0.075 f 1
0.8
Binomial: n = 15, p = 0.005
Poisson: lamda = 0.075
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

36. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.010
Poisson:  = 0.150 f 1
0.8
Binomial: n = 15, p = 0.010
Poisson: lamda = 0.150
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

37. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.015
Poisson:  = 0.225 f 1
0.8
Binomial: n = 15, p = 0.015
Poisson: lamda = 0.225
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

38. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.020
Poisson:  = 0.300 f 1
0.8
Binomial: n = 15, p = 0.020
Poisson: lamda = 0.300
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

39. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.025
Poisson:  = 0.375 f 1
0.8
Binomial: n = 15, p = 0.025
Poisson: lamda = 0.375
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

40. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.030
Poisson:  = 0.450 f 1
0.8
Binomial: n = 15, p = 0.030
Poisson: lamda = 0.450
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

41. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.035
Poisson:  = 0.525 f 1
0.8
Binomial: n = 15, p = 0.035
Poisson: lamda = 0.525
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

42. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.040
Poisson:  = 0.600 f 1
0.8
Binomial: n = 15, p = 0.040 
Poisson: lamda = 0.600
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

43. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.045
Poisson:  = 0.675 f 1
0.8
Binomial: n = 15, p = 0.045
Poisson: lamda = 0.675
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

44. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.050
Poisson:  = 0.750 f 1
0.8
Binomial: n = 15, p = 0.050
Poisson: lamda = 0.750
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

45. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.055
Poisson:  = 0.825 f 1
0.8
Binomial: n = 15, p = 0.055
Poisson: lamda = 0.825
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

46. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.060
Poisson:  = 0.900 f 1
0.8
Binomial: n = 15, p = 0.060
Poisson: lamda = 0.900
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

47. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.065
Poisson:  = 0.975 f 1
0.8
Binomial: n = 15, p = 0.065
Poisson: lamda = 0.975
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

48. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.070
Poisson:  = 1.050 f 1
0.8
Binomial: n = 15, p = 0.070
Poisson: lamda = 1.050
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

49. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.075
Poisson:  = 1.125 f 1
0.8
Binomial: n = 15, p = 0.075
Poisson: lamda = 1.125
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

50. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.080
Poisson:  = 1.200 f 1
0.8
Binomial: n = 15, p = 0.080
Poisson: lamda = 1.200
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

51. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.085
Poisson:  = 1.275 f 1
0.8
Binomial: n = 15, p = 0.085
Poisson: lamda = 1.275
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

52. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.090
Poisson:  = 1.350 f 1
0.8
Binomial: n = 15, p = 0.090
Poisson: lamda = 1.350
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

53. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.095
Poisson:  = 1.425 f 1
0.8
Binomial: n = 15, p = 0.095
Poisson: lamda = 1.425
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

54. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.100
Poisson:  = 1.500 f 1
0.8
Binomial: n = 15, p = 0.100
Poisson: lamda = 1.500
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

55. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.15
Poisson:  = 2.25 f 1
0.8
Binomial: n = 15, p = 0.15
Poisson: lamda = 2.25
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

56. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.20
Poisson:  = 3.00 f 1
0.8
Binomial: n = 15, p = 0.20
Poisson: lamda = 3.00
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

57. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.25
Poisson:  = 3.75 f 1
0.8
Binomial: n = 15, p = 0.25
Poisson: lamda = 3.75
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

58. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.30
Poisson:  = 4.50 f 1
0.8
Binomial: n = 15, p = 0.30
Poisson: lamda = 4.50
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

59. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.35
Poisson:  = 5.25 f 1
0.8
Binomial: n = 15, p = 0.35
Poisson: lamda = 5.25
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

60. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.40
Poisson:  = 6.00 f 1
0.8
Binomial: n = 15, p = 0.40
Poisson: lamda = 6.00
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

61. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.45
Poisson:  = 6.75 f 1
0.8
Binomial: n = 15, p = 0.45
Poisson: lamda = 6.75
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

62. Approximating distributions: Nannestad
Binomial: n = 15, p = 0. 50
Poisson:  = 7.50 f 1
0.8
Binomial: n = 15, p = 0.50
Poisson: lamda = 7.50
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

63. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.55
Poisson:  = 8.25 f 1
0.8
Binomial: n = 15, p = 0.55
Poisson: lamda = 8.25
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

64. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.60
Poisson:  = 9.00 f 1
0.8
Binomial: n = 15, p = 0.60
Poisson: lamda = 9.00
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

65. Approximating distributions: Nannestad
Binomial: n = 15, p = 0.65
Poisson:  = 9.75 f 1
0.8
Binomial: n = 15, p = 0.65
Poisson: lamda = 9.75
0.6
0.4
0.2 x 2 4 6 8 10
Approximating distributions: Nannestad

66. Approximating distributions: Nannestad
Binomial to Poisson
Binomial distribution
Normal distribution
Poisson distribution
Approximating distributions: Nannestad

67. Approximating distributions: Nannestad
Poisson to Normal
Binomial distribution
Normal distribution
Poisson distribution
Approximating distributions: Nannestad

68. Approximating the Poisson distribution with a normal distribution
has discrete data
and looks like
Normal
has continuous data
and looks like
0.2 f
0.2 f
0.15
0.15
0.1
0.1
0.05
0.05 x x 5 10 15 20 5 10 15 20
Approximating distributions: Nannestad

69. Approximating distributions: Nannestad
Why?
When n is large and  >20 the poisson distribution is closely approximated by the normal distribution.
This is a reason tables do not have  values bigger than 20.
Approximating distributions: Nannestad

70. Approximating distributions: Nannestad
Poisson:  = 9.00
Normal: mean = 12.8, VAR = 1.91 f . 1 5 . 1 . 5 x 1 2
Approximating distributions: Nannestad

71. Continuity correction
Approximating distributions: Nannestad

72. Approximating distributions: Nannestad
How?
Approximating distributions: Nannestad

73. Approximating distributions: Nannestad
Poisson:  = 10
Normal: mean = 10, VAR = 10 . 2 f . 1 5 . 1 . 5 x 5 1 1 5 2
Approximating distributions: Nannestad

74. Approximating distributions: Nannestad
Drawing a normal curve with
mean = variance = 9,
and drawing the Poisson and normal distributions together allows comparison.
Approximating distributions: Nannestad

75. Approximating distributions: Nannestad

76. Approximating distributions: Nannestad
Poisson:  = 9
Normal: mean = 9, VAR = 9
0.2 f
0.15
0.1
0.05 x 5 10 15 20
Approximating distributions: Nannestad

77. Approximating distributions: Nannestad
For this value of  = 9 the approximation of a normal curve (mean = variance = 9) is not close,
so in this case we would use values from the Poisson table.
Approximating distributions: Nannestad

78. Approximating distributions: Nannestad

79. Approximating distributions: Nannestad
Why?
When n is large and  >20 the Poisson distribution is closely approximated by values from the normal distribution.
This is a reason tables do not have  values bigger than 20.
Approximating distributions: Nannestad

80. Approximating distributions: Nannestad
Consider how close the normal curve is to the Poisson values as  increases.
When n is large and  >20 the Poisson distribution is closely approximated by the normal distribution.
Approximating distributions: Nannestad

81. Approximating distributions: Nannestad
Poisson:  = 5
Normal: mean = 5, VAR = 5
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

82. Approximating distributions: Nannestad
Poisson:  = 10
Normal: mean = 10, VAR = 10
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

83. Approximating distributions: Nannestad
Poisson:  = 15
Normal: mean = 15, VAR = 15
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

84. Approximating distributions: Nannestad
Poisson:  = 16
Normal: mean = 16, VAR = 16
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

85. Approximating distributions: Nannestad
Poisson:  = 17
Normal: mean = 17, VAR = 17
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

86. Approximating distributions: Nannestad
Poisson:  = 18
Normal: mean = 18, VAR = 18
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

87. Approximating distributions: Nannestad
Poisson:  = 19
Normal: mean = 19, VAR = 19
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

88. Approximating distributions: Nannestad
Poisson:  = 20
Normal: mean = 20, VAR = 20
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

89. Approximating distributions: Nannestad
Poisson:  = 21
Normal: mean = 21, VAR = 21
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

90. Approximating distributions: Nannestad
Poisson:  = 22
Normal: mean = 22, VAR = 22
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

91. Approximating distributions: Nannestad
Poisson:  = 23
Normal: mean = 23, VAR = 23
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

92. Approximating distributions: Nannestad
Poisson:  = 24
Normal: mean = 24, VAR = 24
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

93. Approximating distributions: Nannestad
Poisson:  = 25
Normal: mean = 25, VAR = 25
0.2 f
0.15
0.1
0.05 x 10 20 30
Approximating distributions: Nannestad

94. Approximating distributions: Nannestad
Poisson:  = 25
Normal: mean = 25, VAR = 25
0.1 f
Change scale
0.08
0.06
0.04
0.02 x 10 20 30 40 50
Approximating distributions: Nannestad

95. Approximating distributions: Nannestad
Poisson:  = 30
Normal: mean = 30, VAR = 30
0.1 f
0.08
0.06
0.04
0.02 x 10 20 30 40 50
Approximating distributions: Nannestad

96. Approximating distributions: Nannestad
Poisson:  = 35
Normal: mean = 35, VAR = 35
0.1 f
0.08
0.06
0.04
0.02 x 10 20 30 40 50
Approximating distributions: Nannestad

97. Approximating distributions: Nannestad
Poisson:  = 40
Normal: mean = 40, VAR = 40
0.1 f
0.08
0.06
0.04
0.02 x 10 20 30 40 50
Approximating distributions: Nannestad

98. Approximating distributions: Nannestad
Poisson:  = 40
Normal: mean = 40, VAR = 40
0.1 f
Change scale again
0.08
0.06
0.04
0.02 x 10 20 30 40 50 60 70 80 90
100
Approximating distributions: Nannestad

99. Approximating distributions: Nannestad
Poisson:  = 50
Normal: mean = 50, VAR = 50
0.1 f
0.08
0.06
0.04
0.02 x 10 20 30 40 50 60 70 80 90
100
Approximating distributions: Nannestad

100. Approximating distributions: Nannestad
Poisson:  = 75
Normal: mean = 75, VAR = 75
0.1 f
0.08
0.06
0.04
0.02 x 10 20 30 40 50 60 70 80 90
100
Approximating distributions: Nannestad

101. Approximating distributions: Nannestad
Summary: when can we?
Binomial distribution
Normal distribution
Poisson distribution
np  5 and n(1-p)  5
p is too small for the tables
n large
 > 20
Approximating distributions: Nannestad

102. Approximating distributions: Nannestad
Summary: how do we?
Binomial distribution
Normal distribution
 = np
Poisson distribution
Approximating distributions: Nannestad

103. Approximating distributions: Nannestad
The end.
Approximating distributions: Nannestad