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Chapter 6: Q. 82 (page 404)

Lie detectors A federal report finds that lie detector tests given to truthful persons have probability about 0.2 of suggesting that the person is deceptive. A company asks 12job applicants about thefts from
previous employers, using a lie detector to assess their truthfulness. Suppose that all 12 answer truthfully. Let X=the number of people who the lie detector says are being deceptive.
(a) Find and interpret μX.
(b) Find and interpret σX.

Short Answer

Expert verified

(a) The interpret μX is 2.4.

(b) The interpret σXis 1.3856.

Step by step solution

01

Part (a) Step 1: Given information 

A company asks 12job applicants about thefts from previous employers, using a lie detector to assess their truthfulness .

02

Part (a) Step 2: Explanation 

Let, n=12and p=0.20

The mean of the sample size nand the probability is:

μx=n×p=12(0.20)=2.4

According to the lie detector, on average of 2.4people are deceptive.

03

Part (b) Step 1: Given information 

LetX= the number of people who the lie detector says are being deceptive.

04

Part (b) Step 2: Explanation 

Let, n=12, and p=0.20.

The standard deviation of the sample size nand the probability p:

σx=(n×p)(1-p)

=12(0.20)(1-0.20)

=1.3856

This means that on average, the number of persons who the lie detector claims are lying varies by a factor of two. 1.3856.

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