To estimate how many students out of the population of 700 would request broccoli, we can use proportional reasoning. Here's the step-by-step process:
1. Determine the Proportion of Students Requesting Broccoli:
- In the sample of 120 students, 23 students requested broccoli.
- The proportion of students requesting broccoli in the sample is given by:
[tex]\[
\text{Broccoli Proportion} = \frac{\text{Number of Students Requesting Broccoli}}{\text{Sample Size}} = \frac{23}{120}
\][/tex]
- Calculate [tex]\( \frac{23}{120} \approx 0.19166666666666668 \)[/tex].
2. Estimate the Number of Students in the Whole Population Requesting Broccoli:
- The total population size is 700 students.
- Using the proportion of 0.19166666666666668, we estimate the number of students in the entire population who would request broccoli by multiplying this proportion by the total population size:
[tex]\[
\text{Estimated Students Requesting Broccoli} = \text{Broccoli Proportion} \times \text{Population Size} = 0.19166666666666668 \times 700
\][/tex]
- Calculate [tex]\( 0.19166666666666668 \times 700 \approx 134.16666666666669 \)[/tex].
Given the choices, the closest and most reasonable answer is 134 students.
Therefore, about 134 students out of the 700 would be expected to request broccoli.
