The problem provided in the image asks to calculate Peyton Manning's percentage of completions and percentage of touchdowns based on his statistics over the entire season.

Given Information:

• Week 8 Stats:

  • 215 completed passes
  • 69 touchdowns
  • 25 incomplete passes
  • No interceptions
  • 5,138 yards gained

• Stats for the rest of the season:

  • 71 completed passes
  • 18 touchdowns
  • 23 incomplete passes
  • No interceptions
  • 3,583 yards gained

To find:

1. Completion Percentage: Completion percentage is calculated using: $\text{Completion Percentage} = \left( \frac{\text{Total Completions}}{\text{Total Attempts}} \right) \times 100$ where:

   • Total completions = 215 (Week 8) + 71 (rest of the season)
   • Total attempts = Total completions + Total incomplete passes

2. Touchdown Percentage: Touchdown percentage is calculated using: $\text{Touchdown Percentage} = \left( \frac{\text{Total Touchdowns}}{\text{Total Completions}} \right) \times 100$ where:

   • Total touchdowns = 69 (Week 8) + 18 (rest of the season)

Let me calculate these values.Here are the results for Peyton Manning's statistics:

1. Completion Percentage: 85.63% (rounded to two decimal places)
2. Touchdown Percentage: 30.42% (rounded to two decimal places)

Let me know if you'd like further details or have any questions. Here are some related questions:

1. How is total passing yardage calculated over a season?
2. How would interceptions affect quarterback ratings or completion percentage?
3. What other factors are considered in a quarterback rating system?
4. How is the quarterback's efficiency impacted by the completion percentage?
5. What is the significance of touchdown percentage in assessing a quarterback's performance?

Tip: Always ensure that you're working with the total values for both completions and attempts when calculating percentage-based statistics.