The amount of cleaning solution a company fills its bottles with has a mean of $33 \mathrm{fl} \mathrm{oz}$ and a standard deviation of $1.5 \mathrm{fl} \mathrm{oz}$. The company advertises that these bottles have $32 \mathrm{fl} \mathrm{oz}$ of cleaning solution.

What will be the mean and standard deviation of the distribution of excess cleaning solution, in milliliters?
$(1 \mathrm{fl} \mathrm{oz}$ is approximately $30 \mathrm{~mL}$.
Choose 1 answer:
(A) Mean: $30 \mathrm{~mL}$
Standard deviation: $13 \mathrm{~mL}$
(B) Mean: $30 \mathrm{~mL}$
Standard deviation: $45 \mathrm{~mL}$
(C) Mean: $958 \mathrm{~mL}$
Standard deviation: $13 \mathrm{~mL}$
(D) Mean: $958 \mathrm{~mL}$
Standard deviation: $45 \mathrm{~mL}$

Question

The amount of cleaning solution a company fills its bottles with has a mean of $33 \mathrm{fl} \mathrm{oz}$ and a standard deviation of $1.5 \mathrm{fl} \mathrm{oz}$. The company advertises that these bottles have $32 \mathrm{fl} \mathrm{oz}$ of cleaning solution.

What will be the mean and standard deviation of the distribution of excess cleaning solution, in milliliters?
$(1 \mathrm{fl} \mathrm{oz}$ is approximately $30 \mathrm{~mL}$.
Choose 1 answer:
(A) Mean: $30 \mathrm{~mL}$
Standard deviation: $13 \mathrm{~mL}$
(B) Mean: $30 \mathrm{~mL}$
Standard deviation: $45 \mathrm{~mL}$
(C) Mean: $958 \mathrm{~mL}$
Standard deviation: $13 \mathrm{~mL}$
(D) Mean: $958 \mathrm{~mL}$
Standard deviation: $45 \mathrm{~mL}$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Convert the mean and standard deviation from fluid ounces to milliliters using the conversion factor $1 \text{ fl oz} = 30 \text{ mL}$. ‖ ‖ step 2 ⋮ Calculate the mean of the excess cleaning solution in milliliters: $$ \text{Mean in mL} = (33 \text{ fl oz} - 32 \text{ fl oz}) \times 30 \text{ mL/fl oz} = 1 \text{ fl oz} \times 30 \text{ mL/fl oz} = 30 \text{ mL} $$ ‖ ‖ step 3 ⋮ Calculate the standard deviation of the excess cleaning solution in milliliters: $$ \text{Standard deviation in mL} = 1.5 \text{ fl oz} \times 30 \text{ mL/fl oz} = 45 \text{ mL} $$ ‖ ∻Answer∻ ***D*** ∻Key Concept∻ ⚹Conversion of units and calculation of mean and standard deviation⚹ ∻Explanation∻ ⚹To find the mean and standard deviation of the excess cleaning solution in milliliters, we first convert the given values from fluid ounces to milliliters using the provided conversion factor.⚹◊What is the formula to convert standard deviations between different units of measurement?⍭ Generate me a similar question◊

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