Example 5.20

EXAMPLE 5.20

Probabilities for misclassified sales records. In the audit setting of Example 5.19, what is the probability that the audit finds exactly 10 misclassified sales records? What is the probability that the audit finds no more than 10 misclassified records? Figure 5.14 shows the output from one statistical software system. You see that if the count X has the B(150, 0.08) distribution,

P(X = 10) = 0.106959

P(X ≤ 10) = 0.338427

Figure 5.14 Binomial probabilities, Example 5.20: output from the Minitab statistical software.

It was easy to request these calculations in the software’s menus. For the TI-83/84 calculator, the functions binompdf and binomcdf would be used. In R, the functions dbinom and pbinom would be used. Typically, the output supplies more decimal places than we need and uses labels that may not be helpful (for example, “Probability Density Function” when the distribution is discrete, not continuous). But, as usual with software, we can ignore distractions and find the results we need.