Question

The following table presents the number of vehicles sold in a certain country by several manufacturers in February 2012 and February 2013.
General Motors 2012: 208,489
General Motors 2013: 224,986
Ford 2012: 177,806
Ford 2013: 197,679
Chrysler LLC 2012: 131, 409
Chrysler LLC 2013: 141,869
Toyota 2012: 159,752
Toyota 2013: 166,972
Honda 2012: 108,531
Honda 2013: 110,124
Nissan 2012: 105,953
Nissan 2013: 100,736

Construct a relative frequency distribution for the 2012 sales. Round the answers to at least three decimal places.

Answer 1

To construct a relative frequency distribution for the 2012 vehicle sales, we first need to calculate the total number of vehicles sold in 2012 across all manufacturers.

### Step 1: Calculate Total Sales for 2012

- General Motors: 208,489
- Ford: 177,806
- Chrysler LLC: 131,409
- Toyota: 159,752
- Honda: 108,531
- Nissan: 105,953

**Total Sales in 2012:**

\[
208,489 + 177,806 + 131,409 + 159,752 + 108,531 + 105,953 = 891,940
\]

### Step 2: Calculate the Relative Frequencies

Now, we will calculate the relative frequency for each manufacturer by dividing the number of vehicles sold by the total vehicles sold in 2012.

\[
\text{Relative Frequency} = \frac{\text{Number of Vehicles Sold}}{\text{Total Sales}}
\]

#### Calculations:

1. **General Motors:**
\[
\text{Relative Frequency} = \frac{208,489}{891,940} \approx 0.233
\]

2. **Ford:**
\[
\text{Relative Frequency} = \frac{177,806}{891,940} \approx 0.199
\]

3. **Chrysler LLC:**
\[
\text{Relative Frequency} = \frac{131,409}{891,940} \approx 0.147
\]

4. **Toyota:**
\[
\text{Relative Frequency} = \frac{159,752}{891,940} \approx 0.179
\]

5. **Honda:**
\[
\text{Relative Frequency} = \frac{108,531}{891,940} \approx 0.122
\]

6. **Nissan:**
\[
\text{Relative Frequency} = \frac{105,953}{891,940} \approx 0.119
\]

### Step 3: Present the Relative Frequency Distribution

Now we can summarize the results in a table format.

| Manufacturer | Vehicles Sold (2012) | Relative Frequency |
|--------------------|----------------------|--------------------|
| General Motors | 208,489 | 0.233 |
| Ford | 177,806 | 0.199 |
| Chrysler LLC | 131,409 | 0.147 |
| Toyota | 159,752 | 0.179 |
| Honda | 108,531 | 0.122 |
| Nissan | 105,953 | 0.119 |
| **Total** | **891,940** | **1.000** |

### Note
The relative frequencies have been rounded to three decimal places as requested.