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

44%
44%

58%
58%

40%
40%

47%

Answer 1

To estimate the percentage of students that are already recycling based on the survey results from the three halls, we can calculate the percentage of students recycling in each hall and then find the overall weighted average based on the number of students in each hall.

1. First Hall:

   • Students recycling: 32
   • Total students: 80
   • Percentage = \( \frac{32}{80} \times 100 = 40% \)

2. Second Hall:

   • Students recycling: 48
   • Total students: 110
   • Percentage = \( \frac{48}{110} \times 100 \approx 43.64% \)

3. Third Hall:

   • Students recycling: 49
   • Total students: 85
   • Percentage = \( \frac{49}{85} \times 100 \approx 57.65% \)

Next, we will calculate the total number of students sampled and the total number of students recycling.

• Total students sampled = 80 + 110 + 85 = 275
• Total recycling = 32 + 48 + 49 = 129

Now we can find the overall percentage of students recycling:

\[ \text{Overall percentage} = \frac{129}{275} \times 100 \approx 46.91% \]

Rounding this to the nearest whole number gives approximately 47%. Therefore, the best estimate of the percentage of students that are already recycling is 47%.

So, the answer is 47%.