1. **State the problem:** We are given a two-way table with counts of people who prefer different music genres and shoe types. We need to fill in the total relative frequency table (percentages) based on the counts. 2. **Given data (counts):** \begin{array}{l|cc|c} & \text{Hip Hop} & \text{Rock and Roll} & \text{Total} \\ \hline \text{Basketball Shoes} & 28 & 13 & 41 \\ \text{Crocs} & 6 & 20 & 26 \\ \hline \text{Total} & 34 & 33 & 67 \end{array} 3. **Formula for relative frequency:** $$\text{Relative Frequency} = \frac{\text{Count}}{\text{Total number of people}} \times 100\%$$ 4. **Calculate each cell's relative frequency:** - Basketball Shoes, Hip Hop: $\frac{28}{67} \times 100 \approx 41.79\% \approx 42\%$ - Basketball Shoes, Rock and Roll: $\frac{13}{67} \times 100 \approx 19.40\% \approx 19\%$ - Crocs, Hip Hop: $\frac{6}{67} \times 100 \approx 8.96\% \approx 9\%$ - Crocs, Rock and Roll: $\frac{20}{67} \times 100 \approx 29.85\% \approx 30\%$ 5. **Calculate row totals (relative frequencies):** - Basketball Shoes total: $\frac{41}{67} \times 100 \approx 61.19\% \approx 61\%$ - Crocs total: $\frac{26}{67} \times 100 \approx 38.81\% \approx 39\%$ 6. **Calculate column totals (relative frequencies):** - Hip Hop total: $\frac{34}{67} \times 100 \approx 50.75\% \approx 51\%$ - Rock and Roll total: $\frac{33}{67} \times 100 \approx 49.25\% \approx 49\%$ 7. **Check grand total:** - Total relative frequency should be 100% (sum of all counts divided by total counts times 100). 8. **Final relative frequency table (rounded to nearest whole percent):** \begin{array}{l|cc|c} & \text{Hip Hop} & \text{Rock and Roll} & \text{Total} \\ \hline \text{Basketball Shoes} & 42\% & 19\% & 61\% \\ \text{Crocs} & 9\% & 30\% & 39\% \\ \hline \text{Total} & 51\% & 49\% & 100\% \end{array} This table correctly reflects the relative frequencies based on the original counts. **Note:** The percentages in the user's provided relative frequency table are incorrect (e.g., totals over 100%). Our calculated table is consistent and sums correctly.