/*! 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. 74 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. 74 (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 standard deviation of T is

Short Answer

Expert verified

The random variable indicating the total number of calories in the breakfast's total number of calories has a standard deviation is鈮�11.66

Step by step solution

01

Given information

1- ounces of breakfast cereal :

The mean value is 渭X=110

The variance value is 蟽X=10

Determine 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.)

Red light! Refer to Exercise 84. Calculate and interpret P(Y鈮�7)

Easy-start mower? A company has developed an "easy-start" mower that cranks the engine with the push of a button. The company claims that the probability the mower will start on any push of the button is 0.9. Assume for now that this claim is true. On the next 30 uses of the mower, let T=the number of times it starts on the first push of the button. Here is a histogram of the probability distribution of T :

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

b. Describe the shape of the probability distribution.

Ms. Hall gave her class a 10-question multiple-choice quiz.

Let X=the number of questions that a randomly selected student in the class answered correctly. The computer output gives information about the probability distribution of X. To determine each student鈥檚 grade on the quiz (out of 100), Ms. Hall will multiply his or her number of correct answers by 5and then add 50.Let G=the grade of a randomly chosen student in the class.

Easy quiz

a. Find the median of G.

b. Find the interquartile range (IQR) of G.

Horse pregnanciesBigger animals tend to carry their young longer before birth. The

length of horse pregnancies from conception to birth varies according to a roughly Normal

distribution with mean 336 days and standard deviation 6 days. Let X = the length of a

randomly selected horse pregnancy.

a. Write the event 鈥減regnancy lasts between 325 and 345 days鈥� in terms of X. Then find

this probability.

b. Find the value of c such thatP(X鈮�c)=0.20
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Pure Maths

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Mechanics Maths

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.