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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 μX=110

The variance value is σX=10

Find the cup of whole milk

The mean value is μY=140

The variance value is σY=12

02

Calculations

If X and Y are not mutually exclusive, then

The property of mean is μaX+bY=aμX+bμY

The property of variance is σaX+bY2=a2μX2+b2μY2

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

μT=μX+Y/2=μX+12μY=110+12(140)=180

The resultant variance of T is

σT=σX+Y2=σX2+122σY2=(10)2+14(12)2≈11.66

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Most popular questions from this chapter

Benford’s law Exercise 9 described how the first digits of numbers in legitimate records often follow a model known as Benford’s law. Call the first digit of a randomly chosen legitimate record X for short. The probability distribution for X is shown here (note that a first digit can’t be 0). From Exercise 9, E(X)=3.441. Find the standard deviation of X. Interpret this value.

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