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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? Choose 1 answer: (A) 16 (B) 48 (C) 64 (D) 400

Sicilia randomly selected 25%25\% of the Sound Sleep email subscribers and asked them how many hours of sleep they average each night. Of the subscribers surveyed, 1616 average less than 66 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 66 hours of sleep?\newlineChoose 11 answer:\newline(A) 1616\newline(B) 4848\newline(C) 6464\newline(D) 400400

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Full solution

Q. Sicilia randomly selected 25%25\% of the Sound Sleep email subscribers and asked them how many hours of sleep they average each night. Of the subscribers surveyed, 1616 average less than 66 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 66 hours of sleep?\newlineChoose 11 answer:\newline(A) 1616\newline(B) 4848\newline(C) 6464\newline(D) 400400
  1. Understand Given Information: Understand the given information.\newlineWe know that 25%25\% of the Sound Sleep email subscribers were surveyed, and out of those surveyed, 1616 subscribers average less than 66 hours of sleep each night.
  2. Calculate Total Surveyed Subscribers: Calculate the total number of surveyed subscribers.\newlineSince 1616 subscribers represent 25%25\% of the surveyed group, we can calculate the total number of surveyed subscribers by dividing the number of subscribers who average less than 66 hours of sleep by the percentage they represent.\newlineTotal surveyed subscribers = 160.25\frac{16}{0.25}
  3. Perform Calculation: Perform the calculation from Step 22.\newlineTotal surveyed subscribers = 16/0.25=6416 / 0.25 = 64
  4. Interpret Result: Interpret the result.\newlineThe calculation shows that 6464 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.
  5. Calculate Total Subscribers: Calculate the total number of Sound Sleep email subscribers.\newlineSince the 6464 surveyed subscribers represent 25%25\% of the total number of subscribers, we can calculate the total number of subscribers by multiplying the number of surveyed subscribers by 44 (since 25%25\% is 1/41/4 of 100%100\%).\newlineTotal number of subscribers = 64×464 \times 4
  6. Perform Calculation: Perform the calculation from Step 55.\newlineTotal number of subscribers = 64×4=25664 \times 4 = 256
  7. Estimate Subscribers Less Than 66 Hours: Estimate the number of subscribers who average less than 66 hours of sleep.\newlineSince 1616 out of 6464 surveyed subscribers average less than 66 hours of sleep, we can estimate that the same proportion of the total number of subscribers also average less than 66 hours of sleep.\newlineEstimated number of subscribers who average less than 66 hours = 1664×256\frac{16}{64} \times 256
  8. Perform Calculation: Perform the calculation from Step 77.\newlineEstimated number of subscribers who average less than 66 hours = 1664×256=14×256=64\frac{16}{64} \times 256 = \frac{1}{4} \times 256 = 64

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