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Chapter 6: Q. 81 (page 404)

81. Random digit dialing When an opinion poll calls residential telephone numbers at random, only20% of the calls reach a live person. You watch the random digit dialing machine make 15 calls. Let X= the number of calls that reach a live person.
(a) Find and interpret μX.
(b) Find and interpret σX.

Short Answer

Expert verified

(a) The interpret μXis 3.

(b) The interpret σX is 1.5492.

Step by step solution

01

Part (a) Step 1: Given information 

An opinion poll calls residential telephone numbers at random, only 20%of the calls reach a live person. And the random digit dialing machine make15 calls.

02

Part (a) Step 2: Explanation 

Given: n=15, and p=0.20

The mean of the size nand the probability pis:

μx=n×p

=15(0.20)

=3.

03

Part (b) Step 1: Given information 

Let X= the number of calls that reach a live person.

04

Part (b) Step 2: Explanation 

Given: n=15and p=0.20

The standard deviation is:

σx=(n×p)(1-p)

=15(0.20)(1-0.20)

=1.5492.

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Most popular questions from this chapter

Ms. Hall gave her class a 10-question multiple-choice quiz. Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output below gives information about the probability distribution of X. To determine each student’s grade on the quiz (out of localid="1649489099543" 100), Ms. Hall will multiply his or her number of correct answers by 10. Let localid="1649489106434" G=the grade of a randomly chosen student in the class.

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