It is a striking fact that the first digits of numbers in legitimate records oft

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.

First digit 1 2 3 4 5 6 7 8 9

Proportion 0.28 0.168 0.108 0.079 0.068 0.061 0.04 0.044 0.152

Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's Law holds, that among 1186 randomly chosen invoices there are no more than 687 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)

Explanation / 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 0.28 0.168 0.108 0.079 0.068 0.061 0.04 0.044 0.152

By Benford's Law, P( x <=3) =0.28+0.168+0.108 =0.556

Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's Law holds, that among 1186 randomly chosen invoices there are no more than 687 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)

N=1186, p=0.556 we have to find P( x <= 687)

By using normal approximation to Binomial,

Expectation = np = 659.416

Variance = np(1 - p) = 292.780704

Standard deviation = 17.1108

With continuity correction, z =(687.5-659.416)/ 17.1108 =1.64

P( x <=687) = P( z < 1.64)

=0.9495

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