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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 渭X.
(b) Find and interpret 蟽X.

Short Answer

Expert verified

(a) The interpret 渭Xis 3.

(b) The interpret 蟽X 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:

渭x=n脳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:

蟽x=(n脳p)(1-p)

=15(0.20)(1-0.20)

=1.5492.

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Most popular questions from this chapter

Exercises 47 and 48 refer to the following setting. Two independent random variables Xand Yhave the probability distributions, means, and standard deviations shown.

47. Sum Let the random variableT=X+Y.
(a) Find all possible values of T. Compute the probability that Ttakes each of these values. Summarize the probability distribution ofT in a table.
(b) Show that the mean of Tis equal to渭X+渭Y.
(c) Confirm that the variance of T is equal to 蟽X2+蟽Y2. Show that 蟽T鈮�蟽X+蟽Y.

84. Lie detectors Refer to Exercise 82. Let Y= the number of people who the lie detector says are telling the truth.
(a) Find P(Y鈮�10). How is this related toP(X鈮�2)? Explain.
(b) Calculate 渭Yand蟽Y. How do they compare with 渭Xand 蟽X? Explain why this makes sense.

Refer to the previous Check Your Understanding (page 390 ) about Mrs. Desai's special multiple-choice quiz on binomial distributions. We defined X=the number of Patti's correct guesses.

1. Find 渭X. Interpret this value in context.

In which of the following situations would it be appropriate to use a Normal distribution to approximate probabilities for a binomial distribution with the given values of n and p?

(a)n=10,p=0.5

(b)n=40,p=0.88

(c)n=100,p=0.2

(d)n=100,p=0.99

(e)n=1000,p=0.003

50. Checking independence For each of the following situations, would you expect the random variables Xand Yto be independent? Explain your answers.

(a)Xis the rainfall (in inches) on November 6of this year, and Yis the rainfall at the same location on November 6 of next year.
(b) Xis the amount of rainfall today, and Y is the rainfall at the same location tomorrow.
(c) Xis today's rainfall at the airport in Orlando, Florida, and Y is today's rainfall at Disney World just outside Orlando.
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