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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 1/2 cup of whole milk. Let T be the random variable that represents the total number of calories in this breakfast.

The standard deviation of mathrmT is:

a. 22
b. 16
c. 15.62.
d. 11.66
e. 4

Sagot :

Facundo3141592idn

We want to find the standard deviation of a sum to know the standard deviation on the number of calories on a breakfast.

We will see that the correct option is b; 16.

First, we know that:

  • 1 Lb of cereal has a standard deviation of 10 calories.
  • 1 cup of milk has a standard deviation of 12 calories.

The breakfast is:

1 Lb of cereal and 1/2 cup of milk.

The 1Lb of cereal adds 10 calories to the standard deviation.

And if a cup of milk has a standard deviation of 12 calories, then half a cup has half that standard deviation, so it is 6 calories.

And in addition or subtraction, the standard deviation of the operation is given as the sum of the standard deviation of each element, so the total standard deviation of the breakfast is:

10 calories + 6 calories = 16 calories.

So the correct option is b.

If you want to learn more, you can read:

https://brainly.com/question/12402189

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