Question

Use the following sample to estimate the population proportion of red automobiles in the United States. Cities Red Blue Silver Black White Houston, TX 32 18 4 25 10 Boston, MA 29 36 17 26 46 Las Vegas, NV 23 25 11 39 33 (1 point) Responses 19% 19% 20% 20% 21% 21% 22%

Answer 1

To estimate the population proportion of red automobiles in the United States based on the provided sample data, we first need to calculate the total number of automobiles and the total number of red automobiles from the cities listed.

### Data Breakdown
1. **Houston, TX**:
- Red: 32
- Total = 32 + 18 + 4 + 25 + 10 = 89

2. **Boston, MA**:
- Red: 29
- Total = 29 + 36 + 17 + 26 + 46 = 154

3. **Las Vegas, NV**:
- Red: 23
- Total = 23 + 25 + 11 + 39 + 33 = 131

### Totals
- Total Red = 32 (Houston) + 29 (Boston) + 23 (Las Vegas) = 84
- Total = 89 (Houston) + 154 (Boston) + 131 (Las Vegas) = 374

### Proportion of Red Automobiles
Now we can calculate the population proportion of red automobiles:

\[
\text{Proportion of Red Cars} = \frac{\text{Total Red Cars}}{\text{Total Cars}} = \frac{84}{374}
\]

Calculating this gives:

\[
\text{Proportion of Red Cars} \approx 0.224
\]

### Expressing as a Percentage
To express this proportion as a percentage, multiply by 100:

\[
0.224 \times 100 \approx 22.4\%
\]

### Conclusion
Since the options provided are 19%, 20%, 21%, and 22%, the closest estimate for the population proportion of red automobiles in the United States is **22%**.