Reference no: EM131803962

Internal auditors sometimes check random samples of transactions within a database. Suppose that in a particular set of transactions, 2% contain an error of some kind. The auditor takes a random sample of 20 transactions for checking. Let X denote the number of transactions found to be in error in the sample.

(a) State the probability distribution of X (including the values of all parameters) and find the probability that 2 transactions are found to be in error.   

(b) If three or more transactions are found to be in error then a larger sample is taken for checking. How often will this happen? (Use the appropriate template).

(c) What assumption is required for the validity of the above answers?

Data

Sample size 100

Probability of success 0.2

Statistics

Mean 20

Variance 16

Standard deviation 4

Binomial Probabilities Table

X P(X) Cumulative

0 0.00000 0.00000

1 0.00000 0.00000

2 0.00000 0.00000

3 0.00000 0.00000

4 0.00000 0.00000

5 0.00001 0.00002

6 0.00006 0.00008

7 0.00020 0.00028

8 0.00058 0.00086

9 0.00148 0.00233

10 0.00336 0.00570

11 0.00688 0.01257

12 0.01275 0.02533

13 0.02158 0.04691

14 0.03353 0.08044

15 0.04806 0.12851

16 0.06383 0.19234

17 0.07885 0.27119

18 0.09090 0.36209

19 0.09807 0.46016

20 0.09930 0.55946

21 0.09457 0.65403

22 0.08490 0.73893

23 0.07198 0.81091

24 0.05773 0.86865

25 0.04388 0.91252

26 0.03164 0.94417

27 0.02168 0.96585

28 0.01413 0.97998

29 0.00877 0.98875

30 0.00519 0.99394

31 0.00293 0.99687

32 0.00158 0.99845

33 0.00081 0.99926

34 0.00040 0.99966

35 0.00019 0.99985

36 0.00009 0.99994

37 0.00004 0.99998

38 0.00002 0.99999

39 0.00001 1.00000

40 0.00000 1.00000

41 0.00000 1.00000

42 0.00000 1.00000

43 0.00000 1.00000

44 0.00000 1.00000

45 0.00000 1.00000

46 0.00000 1.00000

47 0.00000 1.00000

48 0.00000 1.00000

49 0.00000 1.00000

50 0.00000 1.00000

51 0.00000 1.00000

52 0.00000 1.00000

53 0.00000 1.00000

54 0.00000 1.00000

55 0.00000 1.00000

56 0.00000 1.00000

57 0.00000 1.00000

58 0.00000 1.00000

59 0.00000 1.00000

60 0.00000 1.00000

61 0.00000 1.00000

62 0.00000 1.00000

63 0.00000 1.00000

64 0.00000 1.00000

65 0.00000 1.00000

66 0.00000 1.00000

67 0.00000 1.00000

68 0.00000 1.00000

69 0.00000 1.00000

70 0.00000 1.00000

71 0.00000 1.00000

72 0.00000 1.00000

73 0.00000 1.00000

74 0.00000 1.00000

75 0.00000 1.00000

76 0.00000 1.00000

77 0.00000 1.00000

78 0.00000 1.00000

79 0.00000 1.00000

80 0.00000 1.00000

81 0.00000 1.00000

82 0.00000 1.00000

83 0.00000 1.00000

84 0.00000 1.00000

85 0.00000 1.00000

86 0.00000 1.00000

87 0.00000 1.00000

88 0.00000 1.00000

89 0.00000 1.00000

90 0.00000 1.00000

91 0.00000 1.00000

92 0.00000 1.00000

93 0.00000 1.00000

94 0.00000 1.00000

95 0.00000 1.00000

96 0.00000 1.00000

97 0.00000 1.00000

98 0.00000 1.00000

99 0.00000 1.00000

100 0.00000 1.00000