/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 73 The number of calories in a 1-ou... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 6: Q. 73 (page 395)

The number of calories in a 1-ounce serving of a certain breakfast cereal is a random variable with mean 110 and standard deviation 10. The number of calories in a cup of whole milk is a random variable with mean 140 and standard deviation 12. For breakfast, you eat 1 ounce of the cereal with 12cup of whole milk. Let T be the random variable that represents the total number of calories in this breakfast.

The mean of T is

Short Answer

Expert verified

The resultant mean T is 180.

Step by step solution

01

Given information

To make one ounce of breakfast cereal,

The mean value is 渭X=110

The variance value is 蟽X=10

Find the cup of whole milk

The mean value is 渭Y=140

The variance value is 蟽Y=12

02

Calculations

If X and Y are not mutually exclusive, then

The property of mean is 渭aX+bY=补渭X+产渭Y

The property of variance is 蟽aX+bY2=a2渭X2+b2渭Y2

T denotes the total number of calories consumed at breakfast ( 1 ounce of the cereal and half cup of whole milk).

That is,

T=X+Y2

As a result, The mean of T is

渭T=渭X+Y/2=渭X+12渭Y=110+12(140)=180

The resultant variance of T is

蟽T=蟽X+Y2=蟽X2+122蟽Y2=(10)2+14(12)2鈮�11.66

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

Most popular questions from this chapter

.Life insurance The risk of insuring one person鈥檚 life is reduced if we insure many people. Suppose that we insure two 21-year-old males, and that their ages at death are independent. If X1andX2are the insurer鈥檚 income from the two insurance policies, the insurer鈥檚 average income W on the two policies is

W=X1+X22=0.5X1+0.5X2

Find the mean and standard deviation of W. (You see that the mean income is the same as for a single policy but the standard deviation is less.)

.Essay errors Typographical and spelling errors can be either 鈥渘onword errors鈥� or 鈥渨ord errors.鈥� A nonword error is not a real word, as when 鈥渢he鈥� is typed as 鈥渢eh.鈥� A word error is a real word, but not the right word, as when 鈥渓ose鈥� is typed as 鈥渓oose.鈥� When students are asked to write a 250-word essay (without spell-checking), the number of nonword errors X has the following probability distribution:

Value of X01234
Probability0.10.20.30.30.1

渭X=2.1蟽X=1.136

Value of Y0123
Probability0.40.30.20.1

渭Y=1.0蟽Y=1.0

a) Find the mean and standard deviation of the difference Y-Xin the number of errors made by a randomly selected student. Interpret each value in context.

(b) Challenge: Find the probability that a randomly selected student makes more word errors than nonword errors .

Sally takes the same bus to work every morning. Let X=the amount of time (in minutes) that she has to wait for the bus on a randomly selected day. The probability distribution of Xcan be modeled by a uniform density curve on the interval from data-custom-editor="chemistry" 0minutesto8minutes. Define the random variable V=60X

a. Explain what Vrepresents.

b. What probability distribution does Vhave?

Where鈥檚 the bus? Sally takes the same bus to work every morning. Let X = the amount of

time (in minutes) that she has to wait for the bus on a randomly selected day. The

probability distribution of X can be modeled by a uniform density curve on the interval

from 0 minutes to8 minutes. Find the probability that Sally has to wait between 2 and 5

minutes for the bus.

Bag check Thousands of travelers pass through the airport in Guadalajara,

Mexico, each day. Before leaving the airport, each passenger must go through the customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "go ahead." Customs agents claim that the light has probability 0.30of showing red on any push of the button. Assume for now that this claim is true. Suppose we watch 20 passengers press the button. Let R=the number who get a red light. Here is a histogram of the probability distribution of R:

a. What probability distribution does R have? Justify your answer.

b. Describe the shape of the probability distribution.
See all solutions

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.