Question

Scores of 70, 75, 80, and 85 are weighted at 10%, 20%, 30%, and 40%.(1 point) The weighted average score is .

Answer 1

To calculate the weighted average score, we will multiply each score by its corresponding weight and then sum these values. Finally, we will divide the total by the sum of the weights.

Here's the calculation:

1. **Scores and their corresponding weights:**
- Score 1: 70, Weight: 10% (0.10)
- Score 2: 75, Weight: 20% (0.20)
- Score 3: 80, Weight: 30% (0.30)
- Score 4: 85, Weight: 40% (0.40)

2. **Calculating the weighted contributions:**
- Contribution from Score 1: \( 70 \times 0.10 = 7.0 \)
- Contribution from Score 2: \( 75 \times 0.20 = 15.0 \)
- Contribution from Score 3: \( 80 \times 0.30 = 24.0 \)
- Contribution from Score 4: \( 85 \times 0.40 = 34.0 \)

3. **Summing the contributions:**
\[
7.0 + 15.0 + 24.0 + 34.0 = 80.0
\]

4. **Sum of the weights:**
\[
0.10 + 0.20 + 0.30 + 0.40 = 1.0
\]

5. **Calculating the weighted average:**
\[
\text{Weighted Average} = \frac{\text{Total Contribution}}{\text{Sum of Weights}} = \frac{80.0}{1.0} = 80.0
\]

Therefore, the weighted average score is **80.0**.