To determine how many students out of the total population would prefer a silver car, we can use proportional reasoning based on the sample data provided.
Let's break down the steps:
1. Identify the relevant data from the sample:
- Total number of students in the sample: 80
- Number of students in the sample who prefer a silver car: 14
2. Find the proportion of students in the sample who prefer a silver car:
- The proportion (or fraction) of the sample that prefers a silver car is calculated as:
[tex]\[
\text{Proportion preferring silver} = \frac{\text{Number of students who prefer silver}}{\text{Total number of students in the sample}} = \frac{14}{80}
\][/tex]
3. Apply the proportion to the total population to estimate the number of students who prefer a silver car:
- Total population of students: 1,000
- Using the proportion from the sample, we multiply it by the total population to get the expected number:
[tex]\[
\text{Expected number of students preferring silver} = \left( \frac{14}{80} \right) \times 1000
\][/tex]
4. Calculate the result:
- Perform the multiplication:
[tex]\[
\left( \frac{14}{80} \right) \times 1000 = 0.175 \times 1000 = 175
\][/tex]
So, using proportional reasoning, we would expect 175 students out of the total 1,000 to prefer a silver car.
