A college dormitory has 24 halls each with 80 to 120 students. To try to increase recycling rates, the dorm head resident takes a sample survey of two halls. In the first hall 32 out of 80 students are already recycling. In the second hall, 48 out of 110 students are already recycling. In the third hall, 49 out of 85 students are already recycling. If the sample surveys are representative of the entire dorm population, which is the best estimate of the percentage of students that are already recycling?(1 point)

Question

Responses

47%
47%

58%
58%

44%
44%

40%

Answer 1

To estimate the percentage of students that are already recycling based on the sample surveys from the three halls, we first need to calculate the recycling rates for each hall and then find the overall percentage for all students surveyed.

1. First hall:

   • Students recycling: 32 out of 80
   • Recycling rate: \( \frac{32}{80} = 0.4 \) or 40%

2. Second hall:

   • Students recycling: 48 out of 110
   • Recycling rate: \( \frac{48}{110} \approx 0.4364 \) or approximately 43.64%

3. Third hall:

   • Students recycling: 49 out of 85
   • Recycling rate: \( \frac{49}{85} \approx 0.5765 \) or approximately 57.65%

Next, let's find the overall recycling percentage across all three halls.

• Total students sampled: \( 80 + 110 + 85 = 275 \)
• Total recycling: \( 32 + 48 + 49 = 129 \)

Overall recycling percentage: \[ \text{Recycling percentage} = \frac{129}{275} \approx 0.4673 \text{ or } 46.73% \]

Rounding this, we can say approximately 47% of students are recycling if the sample is representative of the entire dorm population.

Thus, the best estimate of the percentage of students that are already recycling is 47%.