Q. 76 Suppose that 20,000 married adul... [FREE SOLUTION]

91影视

Introductory Statistics

Barbara Illowsky, Susan Dean

$Math Studyset 91影视 Explanations$ Math

OER 2018 Edition 路 902 pages

ISBN: 9781938168208

Chapter 4: Q. 76 (page 289)

Suppose that $20, 000$ married adults in the United States were randomly surveyed as to the number of children they have. The results are compiled and are used as theoretical probabilities. Let X = the number of children married people have.
a. Find the probability that a married adult has three children.
b. In words, what does the expected value in this example represent?
c. Find the expected value.
d. Is it more likely that a married adult will have two to three children or four to six children? How do you know?

Short Answer

Expert verified

(a) The probability that a married adult has three children.

(b) The expected value represents the average number of children a married people having.

(d) It more likely that a married adult will have two to three children.

Step by step solution

Given information (part a)

Given the results of a survey conducted on the number of children married adults have.

Explanation (part a)

$X$	$P (X)$
$0$	$0.10$
$1$	$0.20$
$2$	$0.30$
$3$	$0.20$
$4$	$0.10$
$5$	$0.05$
$6$ or more	$0.05$
Total	$1$

Because the sum of all probabilities for a random variable is 1, the probability x=3 equals 1-sum of all probabilities.

Given information (part b)

Given the results of a survey conducted on the number of children married adults have.

Explanation (part b)

The expected value in the scenario in question represents the average number of children a married couple has.

Given information (part c)

Given the results of a survey conducted on the number of children married adults have.

Explanation (part c)

$X$	$P (X)$	$X . P (x)$
$0$	$0.10$	$0$
$1$	$0.20$	$0.20$
$2$	$0.30$	$0.60$
$3$	$0.20$	$0.60$
$4$	$0.10$	$0.40$
$5$	$0.05$	$0.25$
$6$ or more	$0.05$	$0.30$
Total	$1$	$2.35$

$E (x) = \underset{}{鈭� [x . P (x)]} E (x) = 2.35$

Given information (part d)

Given the results of a survey conducted on the number of children married adults have.

Explanation (part d)

A married adult with two to three children is more likely to have two to three children than a married adult with four to six children because the likelihood of having two to three children is greater than the probability of having four to six children. A person's chances of having two to three children are 0.50, while his or her chances of having four to six children are 0.20.

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91影视

Short Answer

Step by step solution

Given information (part a)

Explanation (part a)

Given information (part b)

Explanation (part b)

Given information (part c)

Explanation (part c)

Given information (part d)

Explanation (part d)

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