According to Benford\'s law, the probability that the first digit of the amount

Question

According to Benford's law, the probability that the first digit of the amount of a randomly chosen invoice is a 1 or a 2 is 0.477. You examine 82 invoices from a vendor and find that 28 have first digits 1 or 2. If Benford's law holds, the count of 1s and 2s will have the binomial distribution with n 82 and p-0.477. Too few 1s and 2s suggests fraud. What is the approximate probability of 28 or fewer 1s and 2s if the invoices follow Benford's law? (Use the normal approximation. Round your answer to four decimal places.) Do you suspect that the invoice amounts are not genuine? This probability is quite big, so we have no reason to be suspicious This probability is quite small, so we have reason to be suspicious. This probability is quite big, so we have reason to be suspicious This probability is quite small, so we have no reason to be suspicious

Explanation / Answer

p = 0.477
n = 82

mean = np = 82*0.477 = 39.114
sd = sqrt(npq) = sqrt(82 * 0.477 * ( 1- 0.477) = 4.5229

P(x <28)
z = ( x -mean) / sd
= ( 28 - 39.114) / 4.5229
= -2.4573

P(x <28) = P(z <-2.4573) = 0.0070 by using standard normal table

The probability is quite small,so we have reason to be suspicious

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