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

58%
58%

40%
40%

47%
47%

44%

Answer 1

To find the best estimate of the percentage of students that are already recycling, we can calculate the recycling rate for each of the three halls and then find the overall average.

1. First Hall (80 Students):

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

2. Second Hall (110 Students):

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

3. Third Hall (85 Students):

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

Next, we calculate the average recycling rate across the three halls:

• Total number of students in the sample: \( 80 + 110 + 85 = 275 \)
• Total number of students recycling: \( 32 + 48 + 49 = 129 \)

Calculating the overall recycling rate:

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

Now, looking at the options provided:

• 58%
• 40%
• 47%
• 44%

The closest estimate to 46.73% is 47%.

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