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83. Random digit dialing Refer to Exercise 81. Let Y= the number of calls that don鈥檛 reach a live person.

(a) Find the mean of Y. How is it related to the mean of X? Explain why this makes sense.
(b) Find the standard deviation of Y.How is it related to the standard deviation of X? Explain why this makes sense

Short Answer

Expert verified

(a) The mean of Yis Y=15-X=12

(b) The standard deviation of Y is Y=X1.5492

Step by step solution

01

Part (a) Step 1: Given information 

Let Y=the number of calls that don鈥檛 reach a live person.

02

Part (a) Step 2: Explanation

Given: n=15, and p=0.20

Since, Yis equal to X, and the only difference is that the terms "success" and "failure" have been swapped.

The mean for the sample size nand the probabilityp is:
pY=1-pX=1-0.20=0.80
Here, n=15
Y=np=15(0.80)=12

Since, the mean of Yis the sample size ndropped by the mean of X.

03

Part (b) Step 1: Given explanation 

The standard deviation ofYis related to the standard deviation of X.

04

Part (b) Step 2: Explanation 

Given: n=15, and p=0.20

Since, Yis equal to X, and the only distinction is that the terms "success" and "failure" have been swapped.

The standard deviation for the sample size n, and the probability pis,

pY=1-pX=1-0.20=0.80
Here,n=15
Y=(np)(1-p)=15(0.80)(1-0.80)=1.5492

Since, the standard deviation for Xand Yare similar.

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