Answer :
Alright, let's break down the question and solve it step-by-step.
1. Understand the Problem:
- We have a population of 700 students.
- A sample of 120 students has been taken from this population.
- Out of these 120 students, 23 students chose broccoli as their preferred green vegetable.
2. Determine the Proportion:
- First, we need to find out the proportion (or fraction) of students in the sample who prefer broccoli.
- This proportion is calculated as the number of students who chose broccoli divided by the total number of students in the sample:
[tex]\[ \text{Proportion of broccoli-preferring students} = \frac{23}{120} \][/tex]
- This proportion can be approximated as 0.19166666666666668.
3. Scale Up to Population:
- We need to apply this proportion to the entire population to estimate how many students among all 700 would prefer broccoli.
- This is done by multiplying the proportion by the total population:
[tex]\[ \text{Expected number of broccoli-preferring students} = 0.19166666666666668 \times 700 \][/tex]
- Calculating this, we get approximately [tex]\( 134.16666666666669 \)[/tex].
4. Final Answer:
- Since the problem asks for the expected number of students in a whole number, it's customary to either round to the nearest whole number or directly use the given decimal value in reporting.
- Thus, we would expect about 134 students out of the 700 to request broccoli.
So, the correct option is:
- 134 students
1. Understand the Problem:
- We have a population of 700 students.
- A sample of 120 students has been taken from this population.
- Out of these 120 students, 23 students chose broccoli as their preferred green vegetable.
2. Determine the Proportion:
- First, we need to find out the proportion (or fraction) of students in the sample who prefer broccoli.
- This proportion is calculated as the number of students who chose broccoli divided by the total number of students in the sample:
[tex]\[ \text{Proportion of broccoli-preferring students} = \frac{23}{120} \][/tex]
- This proportion can be approximated as 0.19166666666666668.
3. Scale Up to Population:
- We need to apply this proportion to the entire population to estimate how many students among all 700 would prefer broccoli.
- This is done by multiplying the proportion by the total population:
[tex]\[ \text{Expected number of broccoli-preferring students} = 0.19166666666666668 \times 700 \][/tex]
- Calculating this, we get approximately [tex]\( 134.16666666666669 \)[/tex].
4. Final Answer:
- Since the problem asks for the expected number of students in a whole number, it's customary to either round to the nearest whole number or directly use the given decimal value in reporting.
- Thus, we would expect about 134 students out of the 700 to request broccoli.
So, the correct option is:
- 134 students
