Q.74 74. Suppose that the weight of o... [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 7: Q.74 (page 432)

74. Suppose that the weight of open boxes of cereal in a home with children is uniformly distributed from two to six pounds with a mean of four pounds and a standard deviation of 1.1547. We randomly survey 64 homes with children.
a. In words, X=
b. The distribution is
c. In words, $鈭� x$ =
d. $鈭� x ~$
e. Find the probability that the total weight of open boxes is less than 250 pounds.
f. Find the $35 t h$ percentile for the total weight of open boxes of cereal.

Short Answer

Expert verified

a. X is the weight of the cereal boxes that are open

b. $X ~ U (2, 6)$ and uniform

c. $鈭� x$ is the sum of the weight of randomly chosen $64$ boxes.

d. $鈭� X ~ N (256, 9.24)$

e. $0.2581$

f. $252.44$ lbs

Step by step solution

Given Information

The standard deviation is $1.1547$

Mean = $4 l b s$

Sample size = $64$

Explanation Part (a)

X is the weight of the cereal boxes that are open.

Explanation Part (b)

The weight of open boxes of cereal in a home with children is uniformly distributed from two to six pounds .

$鈬� x = 2$ and $y = 6$

Mean = $4 l b s$

Hence,

$X ~ U (2, 6)$

Explanation Part (c)

$鈭� x$ is the sum of the weight of randomly chosen $64$ boxes

Explanation Part (d)

We know,

mean $渭_{x} = 4$

standard deviation $蟽_{x} = 1.1547$

Sample size n = $64$

we know,

$鈭� X ~ N (n 渭_{x}, \sqrt{n} 蟽_{x})$

substituting the values we get,

$渭 \underset{x}{鈭�} 鈥� = n 渭_{x} = 64 脳 4 = 256$

and

蟽 鈭� x

= 蟽_{x} (\sqrt{n}) = 1.1547 脳 \sqrt{64} = 9.24

Hence,

$鈭� X ~ N (256, 9.24)$

Explanation Part (e)

We know,

$鈭� X ~ N (256, 9.24)$

Calculating the probability that the total weight of open boxes is less than $250 l b s$

Using a calculator, we find $P (鈭� x 鈮� 250)$

$P (鈭� x 鈮� 250) = normalcdf (鈭� E 99, 250, 256, 9.24)$

$= 0.2581$

Hence the probability is $0.2581$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

Short Answer

Step by step solution

Given Information

Explanation Part (a)

Explanation Part (b)

Explanation Part (c)

Explanation Part (d)

Explanation Part (e)

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Statistics

Discrete Mathematics

Applied Mathematics

Pure Maths

Mechanics Maths

Decision Maths

Study anywhere. Anytime. Across all devices.