A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of

78, 82, 98, and 92.

Alan received an 88 on his term paper. His final examination score was 86. Use the weighted mean formula to find Alan's average for the course. (Round your answer to one decimal place.)

To calculate Alan's average for the course using the weighted mean formula, we must first assign the weights for each component of his grade and then calculate the weighted average.

### The weights for each component are:
- Each test: 15% (four tests in total)
- Term paper: 20%
- Final examination: 20%

We can write the weighted mean formula as follows:

\[
\text{Weighted Mean} = \left( w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_n \cdot x_n \right)
\]

Where \( w_i \) represents the weight for each grade, and \( x_i \) represents the corresponding score.

Now, applying the dataTo calculate Alan's average for the course using the weighted mean formula, we must first assign the weights for each component of his grade and then calculate the weighted average.

### The weights for each component are:
- Each test: 15% (four tests in total)
- Term paper: 20%
- Final examination: 20%

We can write the weighted mean formula as follows:

\[
\text{Weighted Mean} = \left( w_1 \cdot x_1 + w_2 \cdot x_2 + \cdots + w_n \cdot x_n \right)
\]

Where \( w_i \) represents the weight for each grade, and \( x_i \) represents the corresponding score.

Now, applying the 

- Test 1: \( 78 \) (Weight = 15%)
- Test 2: \( 82 \) (Weight = 15%)
- Test 3: \( 98 \) (Weight = 15%)
- Test 4: \( 92 \) (Weight = 15%)
- Term Paper: \( 88 \) (Weight = 20%)
- Final Exam: \( 86 \) (Weight = 20%)

### Step 1: Convert percentages to decimals for each weight:
- Tests: \( 15\% = 0.15 \)
- Term paper: \( 20\% = 0.20 \)
- Final exam: \( 20\% = 0.20 \)

### Step 2: Calculate the weighted contribution of each component:
- Tests: 
  \[
  0.15 \times 78 = 11.7
  \]
  \[
  0.15 \times 82 = 12.3
  \]
  \[
  0.15 \times 98 = 14.7
  \]
  \[
  0.15 \times 92 = 13.8
  \]
- Term paper: 
  \[
  0.20 \times 88 = 17.6
  \]
- Final exam: 
  \[
  0.20 \times 86 = 17.2
  \]

### Step 3: Add the weighted contributions:
\[
11.7 + 12.3 + 14.7 + 13.8 + 17.6 + 17.2 = 87.3
\]

Thus, Alan's weighted average for the course is \( 87.3 \).

### Final Answer:
Alan's average for the course is **87.3**.

---

Would you like more details or further clarification?

Here are 5 related questions:
1. How do you calculate a weighted mean when the weights are not in percentage form?
2. How does the weighted average change if one test score is much lower than the others?
3. What is the impact of a higher weight on the final grade calculation?
4. How can Alan improve his course average with different test or assignment scores?
5. What if Alan had a fifth test, how would that affect the weighted average?

**Tip:** Always ensure the sum of the weights equals 1 (or 100%) when calculating a weighted average.

A professor grades students on four tests, a term paper, and a final examination. Each test counts as 15% of the course grade. The term paper counts as 20% of the course grade. The final examination counts as 20% of the course grade. Alan has test scores of 78, 82, 98, and 92. Alan received an 88 on his term paper. His final examination score was 86. Use the weighted mean formula to find Alan's average for the course. (Round your answer to one decimal place.)

Learn how to calculate a student's course average using the weighted mean formula. This example problem shows how Alan's test scores of 78, 82, 98, and 92, term paper score of 88, and final exam score of 86 lead to a final course average of 87.3. Suitable for high school students.

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