Question 5.73

5.73 Benford’s law.

We learned in Chapter 4 that there is a striking fact that the first digits of numbers in legitimate records often follow a distribution known as Benford’s law. Here it is:

First digit 1 2 3 4 5 6 7 8 9
Proportion 0.301 0.176 0.125 0.097 0.079 0.067 0.058 0.051 0.046
  1. What is the probability that a randomly chosen invoice has a first digit of 1, 2, or 3?
  2. Suppose 10 invoices are randomly chosen. What is the probability that four or more of the invoices will have a first digit of 1, 2, or 3? Use the binomial formula.
  3. Now do a larger study, examining a random sample of 1000 invoices. Use software to find the exact probability that 620 or more of the invoices have first digits of 1, 2, or 3.
  4. Using Table A and no software, use the Normal approximation with continuity correction to find the probability of part (b).

5.73

(a) 0.602. (b) 0.9467. (c) 0.1290. (d) 0.9474.