1. **State the problem:** We have a two-way frequency table showing the number of bags of corn chips by brand and weight category. We need to convert these counts into relative frequencies (percentages) of the total 179 bags. 2. **Formula:** Relative frequency for each cell is calculated as: $$\text{Relative frequency} = \frac{\text{Frequency in cell}}{\text{Total frequency}} \times 100\%$$ 3. **Calculate each cell's relative frequency:** - Brand A, < 24 oz: $$\frac{12}{179} \times 100 \approx 6.7\% \to 7\%$$ - Brand A, 24 oz: $$\frac{40}{179} \times 100 \approx 22.3\% \to 22\%$$ - Brand A, > 24 oz: $$\frac{10}{179} \times 100 \approx 5.6\% \to 6\%$$ - Brand A, Total: $$\frac{62}{179} \times 100 \approx 34.6\% \to 35\%$$ - Brand B, < 24 oz: $$\frac{9}{179} \times 100 \approx 5.0\% \to 5\%$$ - Brand B, 24 oz: $$\frac{55}{179} \times 100 \approx 30.7\% \to 31\%$$ - Brand B, > 24 oz: $$\frac{15}{179} \times 100 \approx 8.4\% \to 8\%$$ - Brand B, Total: $$\frac{79}{179} \times 100 \approx 44.1\% \to 44\%$$ - Brand C, < 24 oz: $$\frac{7}{179} \times 100 \approx 3.9\% \to 4\%$$ - Brand C, 24 oz: $$\frac{25}{179} \times 100 \approx 14.0\% \to 14\%$$ - Brand C, > 24 oz: $$\frac{6}{179} \times 100 \approx 3.4\% \to 3\%$$ - Brand C, Total: $$\frac{38}{179} \times 100 \approx 21.2\% \to 21\%$$ - Total, < 24 oz: $$\frac{28}{179} \times 100 \approx 15.6\% \to 16\%$$ - Total, 24 oz: $$\frac{120}{179} \times 100 \approx 67.0\% \to 67\%$$ - Total, > 24 oz: $$\frac{31}{179} \times 100 \approx 17.3\% \to 17\%$$ - Total, Total: $$\frac{179}{179} \times 100 = 100\%$$ 4. **Summary:** The relative frequency table rounded to the nearest whole percent is: | Bags contain < 24 oz | Bags contain 24 oz | Bags contain > 24 oz | Total | |---------------------|--------------------|---------------------|-------| | Brand A | 7% | 22% | 6% | 35% | | Brand B | 5% | 31% | 8% | 44% | | Brand C | 4% | 14% | 3% | 21% | | Total | 16% | 67% | 17% | 100% |