Certainly! Let's break down the solution step-by-step.
### 1. Understanding the Data:
- We have two players: Allison Fealey and Emily Janson.
- For each player, we have data on hits, no hits, and total at-bats over two years (junior and senior combined).
### 2. Tabulate the Combined Data:
From the problem, we have the combined data for each player:
| Outcome | A. Fealey | E. Janson |
|---------------|-----------|-----------|
| Hit | 90 | 105 |
| No Hit | 200 | 215 |
| Total At Bats | 290 | 320 |
### 3. Calculating Batting Averages:
The batting average is calculated as the number of hits divided by the total number of at-bats. We need to calculate this for each player.
#### a. Batting Average for Allison Fealey:
- Hits: 90
- Total At Bats: 290
[tex]\[
\text{Batting Average (Fealey)} = \frac{\text{Hits}}{\text{Total At Bats}} = \frac{90}{290} \approx 0.3103
\][/tex]
#### b. Batting Average for Emily Janson:
- Hits: 105
- Total At Bats: 320
[tex]\[
\text{Batting Average (Janson)} = \frac{\text{Hits}}{\text{Total At Bats}} = \frac{105}{320} \approx 0.3281
\][/tex]
### 4. Summary of Batting Averages:
We now have the batting averages for the combined two years:
| Player | Batting Average |
|-----------------|---------------------|
| Allison Fealey | 0.3103 |
| Emily Janson | 0.3281 |
### 5. Determining the Scholarship Award:
Based on their batting averages, Emily Janson has a higher batting average (0.3281) compared to Allison Fealey (0.3103).
### Conclusion:
Emily Janson has the better batting average over the combined junior and senior years and should therefore be awarded the scholarship.
