Sicilia randomly selected $25\%$ of the Sound Sleep email subscribers and asked them how many hours of sleep they average each night. Of the subscribers surveyed, $16$ average less than $6$ hours of sleep each night. Based on the data, what is the most reasonable estimate of the number of Sound Sleep email subscribers who average less than $6$ hours of sleep? $\newline$ Choose $1$ answer: $\newline$ (A) $16$ $\newline$ (B) $48$ $\newline$ (C) $64$ $\newline$ (D) $400$

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Q. Sicilia randomly selected

25\%

of the Sound Sleep email subscribers and asked them how many hours of sleep they average each night. Of the subscribers surveyed,

16

average less than

6

hours of sleep each night. Based on the data, what is the most reasonable estimate of the number of Sound Sleep email subscribers who average less than

6

hours of sleep?

\newline

Choose

1

answer:

\newline

(A)

16

\newline

(B)

48

\newline

(C)

64

\newline

(D)

400

Understand Given Information: Understand the given information. $\newline$ We know that $25\%$ of the Sound Sleep email subscribers were surveyed, and out of those surveyed, $16$ subscribers average less than $6$ hours of sleep each night.
Calculate Total Surveyed Subscribers: Calculate the total number of surveyed subscribers. $\newline$ Since $16$ subscribers represent $25\%$ of the surveyed group, we can calculate the total number of surveyed subscribers by dividing the number of subscribers who average less than $6$ hours of sleep by the percentage they represent. $\newline$ Total surveyed subscribers = $\frac{16}{0.25}$
Perform Calculation: Perform the calculation from Step $2$ . $\newline$ Total surveyed subscribers = $16 / 0.25 = 64$
Interpret Result: Interpret the result. $\newline$ The calculation shows that $64$ subscribers were surveyed in total. However, this is not the final answer we are looking for. We need to estimate the total number of Sound Sleep email subscribers based on the data.
Calculate Total Subscribers: Calculate the total number of Sound Sleep email subscribers. $\newline$ Since the $64$ surveyed subscribers represent $25\%$ of the total number of subscribers, we can calculate the total number of subscribers by multiplying the number of surveyed subscribers by $4$ (since $25\%$ is $1/4$ of $100\%$ ). $\newline$ Total number of subscribers = $64 \times 4$
Perform Calculation: Perform the calculation from Step $5$ . $\newline$ Total number of subscribers = $64 \times 4 = 256$
Estimate Subscribers Less Than $6$ Hours: Estimate the number of subscribers who average less than $6$ hours of sleep. $\newline$ Since $16$ out of $64$ surveyed subscribers average less than $6$ hours of sleep, we can estimate that the same proportion of the total number of subscribers also average less than $6$ hours of sleep. $\newline$ Estimated number of subscribers who average less than $6$ hours = $\frac{16}{64} \times 256$
Perform Calculation: Perform the calculation from Step $7$ . $\newline$ Estimated number of subscribers who average less than $6$ hours = $\frac{16}{64} \times 256 = \frac{1}{4} \times 256 = 64$