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 using the provided sample data, we first need to calculate the total number of cars observed and the total number of red cars in the sample.

Let's sum the number of automobiles in each city:

**Houston, TX:**
- Red: 32
- Blue: 18
- Silver: 4
- Black: 25
- White: 10
- Total = \(32 + 18 + 4 + 25 + 10 = 89\)

**Boston, MA:**
- Red: 29
- Blue: 36
- Silver: 17
- Black: 26
- White: 46
- Total = \(29 + 36 + 17 + 26 + 46 = 154\)

**Las Vegas, NV:**
- Red: 23
- Blue: 25
- Silver: 11
- Black: 39
- White: 33
- Total = \(23 + 25 + 11 + 39 + 33 = 131\)

Now, calculate the total number of red cars and the total number of cars in all three cities:

**Total Red Cars:**
\[
32 + 29 + 23 = 84
\]

**Total Cars:**
\[
89 + 154 + 131 = 374
\]

Now we calculate the proportion of red cars:
\[
\text{Proportion of red cars} = \frac{\text{Total Red Cars}}{\text{Total Cars}} = \frac{84}{374} \approx 0.224
\]

To express this proportion as a percentage:
\[
0.224 \times 100 \approx 22.4\%
\]

So, based on the available responses, the best estimate for the population proportion of red automobiles in the United States using this sample is **22%**.