Question

paisley randomly surveys 48 teachers about the type of car they drive.

if paisely randomly surveys another 300 teachers, how many would she expect to drive an suv?

45
94
15
163

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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"concepts_used": [
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"new_concepts": [],
"current_concepts": [
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"Random Sampling"
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}
</pre_analysis>

<reasoning>

Identify the proportion of SUV drivers in the initial sample

\[

$$\begin{aligned} &\text{Total surveyed } (N) = 48 \\ &\text{SUV count } (s) = 15 \\ &\text{Proportion } (p) = \frac{15}{48} = \frac{5}{16} \end{aligned}$$

\]

Calculate the expected number of SUV drivers in the new sample

\[

$$\begin{aligned} &\text{New sample size } (M) = 300 \\ &\text{Expected SUVs } (E) = 300 \times \frac{5}{16} = \frac{1500}{16} = 93.75 \end{aligned}$$

\]

Round to the nearest whole number

\[
E \approx 94
\]
</reasoning>

<answer>
<mcq-option>45</mcq-option>
<mcq-correct>94</mcq-correct>
<mcq-option>15</mcq-option>
<mcq-option>163</mcq-option>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Sample Predictions",
"Proportional Relationships"
],
"new_concepts": [],
"current_concepts": [
"Sample Predictions",
"Proportional Relationships",
"Random Sampling"
]
}
</pre_analysis>

<reasoning>

Identify the proportion of SUV drivers in the initial sample

\[

$$\begin{aligned} &\text{Total surveyed } (N) = 48 \\ &\text{SUV count } (s) = 15 \\ &\text{Proportion } (p) = \frac{15}{48} = \frac{5}{16} \end{aligned}$$

\]

Calculate the expected number of SUV drivers in the new sample

\[

$$\begin{aligned} &\text{New sample size } (M) = 300 \\ &\text{Expected SUVs } (E) = 300 \times \frac{5}{16} = \frac{1500}{16} = 93.75 \end{aligned}$$

\]

Round to the nearest whole number

\[
E \approx 94
\]
</reasoning>

<answer>
<mcq-option>45</mcq-option>
<mcq-correct>94</mcq-correct>
<mcq-option>15</mcq-option>
<mcq-option>163</mcq-option>
</answer>

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