Question

Using Benford's law According to Benford's law (Exercise 5, page 353 ), the probability that the first digit of the amount on a randomly chosen invoice is a $1$or a $2$is $0.477$. Suppose you examine an SRS of $90$invoices from a vendor and find $29$that have first digits $1$or $2$. Do you suspect that the invoice amounts are not genuine? Compute an appropriate probability to support your answer.

Short answer

The appropriate probability is$P(X\le 29)\approx 0.0021=0.21\%$

Step-by-step solution

Given Information 

The probability that the first digit of the amount on a randomly chosen invoice is a $1$or a $2$$=0.477$

Number of SRS invoices$=90$

Explanation 

Given:

$p=0.477$

$n=90$

Definition binomial probability:

$P(X=k)=\left(\begin{array}{l}n\\ k\end{array}\right)·p^k·(1-p{)}^{n-k}$

Add the corresponding probabilities:

localid="1650032592085" $$\begin{gathered} P(X\le 29)=P(X=0)+P(X=1)+\dots +P(X=29) \\ \approx 0.0021 \\ =0.21\% \end{gathered}$$