Math / Data & Statistics

Question\begin{tabular}{l} $\frac{y}{0}$ \\ \hline \end{tabular}
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 mean of $T$ is 110 140 250 180 195

Studdy Solution

STEP 1

1. The number of calories in the cereal and milk are independent random variables.
2. The mean of the sum of independent random variables is the sum of their means.
3. You consume 1 ounce of cereal and $\frac{1}{2}$ cup of milk.

STEP 2

1. Determine the mean calories from the cereal.
2. Determine the mean calories from $\frac{1}{2}$ cup of milk.
3. Calculate the mean of the total calories $T$ .

STEP 3

The mean number of calories from the cereal is given as:
$\mu_{\text{cereal}} = 110$

STEP 4

The mean number of calories in a full cup of milk is given as:
$\mu_{\text{milk}} = 140$
Since you consume $\frac{1}{2}$ cup of milk, the mean calories from the milk is:
$\mu_{\frac{1}{2} \text{ cup milk}} = \frac{1}{2} \times 140 = 70$

STEP 5

The mean of the total calories $T$ is the sum of the mean calories from the cereal and $\frac{1}{2}$ cup of milk:
$\mu_{T} = \mu_{\text{cereal}} + \mu_{\frac{1}{2} \text{ cup milk}} = 110 + 70 = 180$
The mean of $T$ is:
$\boxed{180}$

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms