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:

Balance Sheet

An account statement depicting the financial position of a company through its assets, obligations, and equity of shareholders at a certain time.

Revenue

The total amount of income generated by the sale of goods or services related to a company’s primary operations.

Cash

Currency and coins that are legal tender, including money deposited in checking accounts and obtainable on demand.

Income Statement

A financial statement that shows a company's revenues and expenses, culminating in the net income for a specific period.