Chapter 6.3, Problem 100E

(a)

To determine

To calculate; the number of invoices to be examined until the one beginning with $\text{8 or 9}$ is spotted.

Answer to Problem 100E

  ${\sigma }_X=9.797$

Explanation of Solution

Given;

  $p=0.097$

Explanation;

  $\begin{array}{l}\text{Definition Geometric Probability:}\\ $ {\text{P(X = k) = q}}^{k-1}\times p={(1-p)}^{k-1}p$\end{array}$

  ${\sigma }_X=\frac{\sqrt{1-0.097}}{0.097}=9.797$

Let’s consider that a large number of invoices are selected randomly. Then, the number of invoices to be examined until the one beginning with eight or nine is spotted would vary $9.767$ invoices around the mean of $10.31$ invoices.

(b)

To determine

To calculate; if it can be suspected that the invoice amounts are not genuine.

Answer to Problem 100E

Not genuine.

  $\text{P(X }\ge \text{ 40) = 1}\text{.87\%}$

Explanation of Solution

Given;

  $p=0.097$

Explanation;

  $\begin{array}{l}\text{Definition Geometric Probability:}\\ $ {\text{P(X = k) = q}}^{k-1}\times p={(1-p)}^{k-1}p$\end{array}$

  $\begin{array}{l}\text{P(X }\ge \text{ 40) = 1 - P(X < 40) = 1 - P(X = 1) - P(X = 2) - }\mathrm{...}\text{ - P(X = 39) }\\ \text{= 1 - 0}\text{.9813 = 0}\text{.0187 = 1}\text{.87\%}\end{array}$

As the probability is smaller than $5\%$ , it can be said that the invoice amounts are not genuine.