Question

kai randomly surveys eighth graders at his school and learns that 7 of 35 respondents own a video gaming system. based on these data, how many of the 150 eighth-grade students in kais school would be expected to own a video gaming system?

15 students
25 students
30 students
50 students

Explanation:

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"new_concepts": [
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</pre_analysis>

<reasoning>

Calculate the sample proportion

\[
p = \frac{7}{35} = \frac{1}{5} = 0.2
\]

Apply proportion to the total population

\[
\text{Expected students} = 150 \times \frac{1}{5} = 30
\]
</reasoning>

<answer>
<mcq-option>15 students</mcq-option>
<mcq-option>25 students</mcq-option>
<mcq-correct>30 students</mcq-correct>
<mcq-option>50 students</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
"Sample Predictions"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
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"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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],
"new_concepts": [
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],
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"Sample Predictions"
]
}
</pre_analysis>

<reasoning>

Calculate the sample proportion

\[
p = \frac{7}{35} = \frac{1}{5} = 0.2
\]

Apply proportion to the total population

\[
\text{Expected students} = 150 \times \frac{1}{5} = 30
\]
</reasoning>

<answer>
<mcq-option>15 students</mcq-option>
<mcq-option>25 students</mcq-option>
<mcq-correct>30 students</mcq-correct>
<mcq-option>50 students</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Statistics",
"Sample Predictions"
]
}
</post_analysis>