Question

A college dormitory has 24 Halls each with 80 to 100 students to try to increase recycling rates the dorm had resident takes a sample survey of two halls in the first Hall 32 out of 80 students are already recycling and 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 44% 58% 47% 40%

Answer 1

To find the best estimate of the percentage of students that are already recycling across the dormitory, we can calculate the percentage of students recycling in each sampled hall and then take the average of those percentages.

1. First Hall:

   • Students recycling = 32
   • Total students = 80
   • Recycling percentage = (32 / 80) * 100 = 40%

2. Second Hall:

   • Students recycling = 48
   • Total students = 110
   • Recycling percentage = (48 / 110) * 100 ≈ 43.64%

3. Third Hall:

   • Students recycling = 49
   • Total students = 85
   • Recycling percentage = (49 / 85) * 100 ≈ 57.65%

Now we can average these percentages:

\[ \text{Average recycling percentage} = \frac{(40 + 43.64 + 57.65)}{3} ≈ \frac{141.29}{3} ≈ 47.10% \]

Now looking at the options of estimates available: 44%, 58%, 47%, and 40%.

The best estimate among these would be 47%. Thus, the final answer is:

47%