A vending machine that serves coffee pours a varying amount of liquid into a cup with varying mass. Assume that the masses of the liquid and the cup are independent.

Here are summary statistics for the masses of the liquid and the cups:
\begin{tabular}{lrr}
& Mean & Standard deviation \
\hline Liquid & $\mu_{L}=250 \mathrm{~g}$ & $\sigma_{L}=20 \mathrm{~g}$ \
Cup & $\mu_{C}=150 \mathrm{~g}$ & $\sigma_{C}=10 \mathrm{~g}$
\end{tabular}

Let $T=$ the total mass of a randomly selected cup filled with liquid from this machine.

Find the mean of $T$.
$\mu_{T}=$ $\square$ grams

Question

A vending machine that serves coffee pours a varying amount of liquid into a cup with varying mass. Assume that the masses of the liquid and the cup are independent.

Here are summary statistics for the masses of the liquid and the cups:
\begin{tabular}{lrr} 
& Mean & Standard deviation \
\hline Liquid & $\mu_{L}=250 \mathrm{~g}$ & $\sigma_{L}=20 \mathrm{~g}$ \
Cup & $\mu_{C}=150 \mathrm{~g}$ & $\sigma_{C}=10 \mathrm{~g}$
\end{tabular}

Let $T=$ the total mass of a randomly selected cup filled with liquid from this machine.

Find the mean of $T$.
$\mu_{T}=$ $\square$ grams

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ To find the mean of $T$, which is the total mass of a randomly selected cup filled with liquid, we need to add the mean mass of the liquid ($\mu_L$) and the mean mass of the cup ($\mu_C$). ‖ ‖ step 2 ⋮ Given that $\mu_L = 250$ grams and $\mu_C = 150$ grams, we calculate the mean of $T$ as follows: $\mu_T = \mu_L + \mu_C$. ‖ ‖ step 3 ⋮ Substituting the given values into the equation from step 2, we get $\mu_T = 250 ext{ g} + 150 ext{ g}$. ‖ ‖ step 4 ⋮ Calculating the sum, we find that $\mu_T = 400 ext{ g}$. ‖ ∻Answer∻ ⚹ $\mu_T = 400$ grams ⚹ ∻Key Concept∻ ⚹Mean of Independent Random Variables⚹ ∻Explanation∻ ⚹The mean of the total mass $T$ is the sum of the means of the independent masses of the liquid and the cup.⚹◊What is the formula for calculating the mean of the total mass (T) of a cup filled with liquid from the coffee vending machine?⍭ Generate me a similar question◊

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