To calculate the student's average for the course using the weighted mean formula, we apply each component's weight to the score and sum them.

Here's a breakdown of the calculation based on the provided weights:

1. Tests: Each test is worth 15%, so the total weight for the tests is $4 \times 15\% = 60\%$.

   • Test scores: 82, 86, 94, 84
   • Weighted contribution from tests: $\left(\frac{82 + 86 + 94 + 84}{4}\right) \times 0.60 = 86.5 \times 0.60 = 51.9$

2. Term Paper: Worth 20% of the course grade.

   • Term paper score: 88
   • Weighted contribution from the term paper: $88 \times 0.20 = 17.6$

3. Final Examination: Worth 20% of the course grade.

   • Final exam score: 84
   • Weighted contribution from the final exam: $84 \times 0.20 = 16.8$

Now, sum these weighted contributions:

$51.9 + 17.6 + 16.8 = 86.3$

So, the student's weighted average for the course is 86.3.

Let me know if you need further clarification!

Here are some additional questions to deepen your understanding:

1. How would the final average change if the term paper was weighted differently?
2. What if the student scored higher on the final exam? How would that affect the outcome?
3. If the test weights were adjusted to 10% each, how would the calculation differ?
4. How does rounding at intermediate steps impact the final result?
5. What if each test had a unique weight?

Tip: Always double-check weight distributions to ensure they sum to 100% when using the weighted mean formula.