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 1187 randomly chosen invoices there are no more than 683 in amounts with first digit 1, 2, or 3? (Round your answer to four decimal places.)

First digit 1 2 3 4 5 6 7 8 9 Proportion 0.291 0.179 0.125 0.087 0.056 0.066 0.049 0.048 0.099

Explanation / Answer

P(1,2,3) = 0.291+0.179+0.125 = 0.595

We first get the z score for the critical value:          
          
x = critical value =    683.5      
u = mean = np =    694.395      
          
s = standard deviation = sqrt(np(1-p)) =    16.97568629      
          
Thus, the corresponding z score is          
          
z = (x-u)/s =    -0.641800267      
          
Thus, the left tailed area is          
          
P(z <   -0.641800267   ) =    0.260501438 [ANSWER]

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.