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Sagot :
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.
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.
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