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.

Fake records usually have fewer first digits 1, 2, and 3. What is the approximate probability, if Benford's Law holds, that among 1152 randomly chosen invoices there are no more than 672 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)

0.8888 was the answer I got and was inncorrect.

First digit 1 2 3 4 5 6 7 8 9 Proportion 0.305 0.184 0.112 0.074 0.053 0.068 0.031 0.034 0.139

Explanation / Answer

Probability that the first digit is 1, 2 or 3 = p = 0.305 + 0.184 + 0.112 = 0.601

n = 1152, p = 0.601, q = 1 - p = 0.399

= np = 692.352, = (npq) = 525.59

z = (x - )/ = (672 - 692.352)/525.59 = -0.0387

P(x 672) = P(z < -0.0387) = 0.4846

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