5.70 Caught doctoring the books After the major accounting scandals with Enron, a large energy company, the question may be posed, “Was there any way to examine Enron’s accounting books to determine if they had been doctored?”

One way uses Benford’s law, which states that in a variety of circumstances, numbers as varied as populations of small towns, figures in a newspaper or magazine, and tax returns and other business records begin with the digit 1 more often than other digits. This law states that the probabilities for the digits 1 through 9 are approximately:

a. If we were to randomly pick one of the digits between 1 and 9 using a random number table or software, what is the probability for each digit?

b. When people attempt to fake numbers, there’s a tendency to use 5 or 6 as the initial digit more often than predicted by Benford’s law. What is the probability of 5 or 6 as the first digit by (i) Benford’s law and (ii) random selection?

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1 2 3 4 5 67 89 Digit Probability 0.30 0.18 0.12 0.10 0.08 0.07 0.06 0.05 0.04