While reading through this year\'s Arkansas Democrat-Gazette newspapers, you rec

Question

While reading through this year's Arkansas Democrat-Gazette newspapers, you record all numbers appearing in a news article-the number of wins by a football team, the total charitable contribution of a politician, the income of a CEO, and so on. Now consider the leading digit of each number. Initially. you might think the leading digit of a randomly selected number would be equally likely to be any of the values (a discrete uniform distribution). However, evidence suggests an alternative probability distribution called Benford's Law: fx(x)= R 1st digit is x)= log10(1 +-), x = 1,2, ,9 What is the probability that the leading digit is at least 8? (Report answer to three decimal places. Answer must be within +-0.001 of correct value.)

Explanation / Answer

probability that leading digit is at least 8 =P(X=8)+P(X=9) =log(1+1/8)+log(1+1/9) =0.097

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