A large bakery uses a machine to dispense frosting onto its cookies. A certain type of cookie gets 4 dots of frosting on top of each cookie. The dots of frosting have a mean mass of $\mu=3$ grams and a standard deviation of $\sigma=0.25$ grams. We can assume that the masses of the dots of frosting are independent from each other. Let $T$ be the total mass of the dots of frosting on a randomly chosen cookie.

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

Question

A large bakery uses a machine to dispense frosting onto its cookies. A certain type of cookie gets 4 dots of frosting on top of each cookie. The dots of frosting have a mean mass of $\mu=3$ grams and a standard deviation of $\sigma=0.25$ grams. We can assume that the masses of the dots of frosting are independent from each other. Let $T$ be the total mass of the dots of frosting on a randomly chosen cookie.

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

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the given information: Each dot of frosting has a mean mass of $ \mu = 3 $ grams and a standard deviation of $ \sigma = 0.25 $ grams. There are 4 dots of frosting on each cookie. ‖ ‖ step 2 ⋮ Since the masses of the dots are independent, the mean of the total mass $ T $ of the frosting on a cookie is the sum of the means of the individual dots. ‖ ‖ step 3 ⋮ Calculate the mean of $ T $: $$ \mu_{T} = 4 imes \mu = 4 imes 3 = 12 ext{ grams} $$ ‖ ∻Answer∻ ⚹ $ \mu_{T} = 12 $ grams ⚹ ∻Key Concept∻ ⚹ The mean of the sum of independent random variables is the sum of their means. ⚹ ∻Explanation∻ ⚹ Since the dots of frosting are independent, the total mean mass is simply the sum of the means of the individual dots. ⚹◊What is the formula to calculate the mean of T, given the mean mass and standard deviation of the frosting dots⍭ Generate me a similar question◊

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