1) Benford\'s Law: It is a striking fact that the first digits of numbers in leg

Question

1) Benford's Law: 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. Firstdigit Proportion 0.284 0.184 0.132 0.075 0.058 0.07 0.039 0.047 0.111 1 2 3456 789 Fake records usually have fewer first digits 1, 2, and 3. Let X be the umber of amounts with first digit 1 2, or 3 among 1231 randomly chosen expense reports, where Benford's Law holds. a) Formulate the exact value of P(X = 682). [10 pts) b) What is the probability that there are no more than 682 in amounts with first digit 1, 2, or 3. (Round your answer to four decimal places.) 10 pts c) What would be your conclusion about the truthfulness of the expense reports? [5 pts

Explanation / Answer

(a) Here P(X = 1,2,3) = 0.284 + 0.184 + 0.132 = 0.6

n = 1231

so here the distribution is binomial distribution

Pr(X = 682) = 1231C682 (0.6)682 (0.4)1231-682 = 0

(b) Pr(X =< 682) = BINOMDIST(x <= 682 ; 1231; 0.6) = 0.0001

(c) Here as the given probability is very less so we would reject the truthfulness of the report,

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