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Out of a population of 700 students, 120 were asked by a random sampling to choose the green vegetable they would have served in the cafeteria. Their responses are shown in the table below.

\begin{tabular}{|c|c|}
\hline
\multicolumn{2}{|c|}{Cafeteria Choices} \\
\hline
Green Vegetable & \begin{tabular}{c}
Number of \\
Students
\end{tabular} \\
\hline
peas & 34 \\
\hline
green beans & 27 \\
\hline
broccoli & 23 \\
\hline
zucchini & 18 \\
\hline
brussels sprouts & 18 \\
\hline
\end{tabular}

Using proportional reasoning, about how many students out of the 700 would you expect to request broccoli?

A. 23 students
B. 30 students
C. 105 students
D. 134 students



Answer :

GinnyAnswer
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.

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