It is a striking fact that the first digits of numbers in legitimate records oft
ID: 3208728 • Letter: I
Question
It is a striking fact that the first digits of numbers in legitimate records often follow a distribution known as Benford's Law, shown below.
Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's Law holds, that among 1209 randomly chosen invoices there are no more than 681 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)
First digit 1 2 3 4 5 6 7 8 9 Proportion 0.293 0.186 0.11 0.083 0.051 0.058 0.033 0.04 0.146Explanation / Answer
Result:
It is a striking fact that the first digits of numbers in legitimate records often follow a distribution known as Benford's Law, shown below.
First digit
1
2
3
4
5
6
7
8
9
Proportion
0.293
0.186
0.11
0.083
0.051
0.058
0.033
0.04
0.146
Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's Law holds, that among 1209 randomly chosen invoices there are no more than 681 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)
p = P( fewer first digits 1, 2, and 3) =0.293+0.186+0.110 =0.589
n=1209
using Binomial distribution,
Expectation = np = 712.101
Variance = np(1 - p) = 292.673511
Standard deviation = 17.1077
Z value for 681, z =(681-712.101)/ 17.1077 = -1.82
P( x 681) = P( z <-1.82)
=0.0344
First digit
1
2
3
4
5
6
7
8
9
Proportion
0.293
0.186
0.11
0.083
0.051
0.058
0.033
0.04
0.146
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