Suppose That a Polygraph Is 90% Accurate (It Will Correctly

question 51

Essay

Suppose that a polygraph is 90% accurate (it will correctly detect 90% of people who are lying and it will
correctly detect 90% of people who are telling the truth). The 2000 employees of a company are given a
polygraph test during which they are asked whether they have been stealing from the company. All of them
deny stealing, when in fact 1% of the employees actually have been stealing. Assume that anyone whom the
polygraph operator finds untruthful is accused of lying. $$\begin{array} { l | c c c } & \text { Thief } & \text { Not a thief } & \text { Total } \\\hline \text { Test finds employees lying } & 18 & 198 & 216 \\\text { Test finds employee truthful } & 2 & 1782 & 1784 \\\text { Total } & 20 & 1980 & 2000\end{array}$$
a. How many employees are accused of lying? Of theses, how many were actually lying and how many were telling
the truth? What percentage of those accused of lying were falsely accused?
b. How many employees are found truthful? Of these, how many were actually truthful? What percentage of those
found truthful were really truthful?

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Definitions:

Weighted Average Method

A cost accounting method that calculates the cost of goods sold and ending inventory based on the weighted average cost of all items available for sale.

Lotions and Cosmetic Manufacturer

A type of business that specializes in producing health and beauty products, including creams, lotions, and makeup.

Job Order Cost System

An accounting system used to track the costs related to a specific job or batch of goods.

Process Cost System

An economic tracking system utilized for attributing costs to analogous products manufactured in large quantities and in a steady flow.