Questions: In a statistics class, John earned the following grades which are weighted as indicated towards the course grade. Compute John's course grade. Item Grade Weight Homework 95 20% Quizzes 78 15% Midterm Exam 85 30% Final Exam 90 35%

Solution Steps

To compute John's course grade, we need to calculate the weighted average of his grades. Each grade is multiplied by its corresponding weight, and then the results are summed up to get the final course grade.

John's grades and their corresponding weights are given as follows:

• Homework: \(95\) with a weight of \(20\%\)
• Quizzes: \(78\) with a weight of \(15\%\)
• Midterm Exam: \(85\) with a weight of \(30\%\)
• Final Exam: \(90\) with a weight of \(35\%\)

The weights are converted from percentages to decimal form:

• Homework: \(0.20\)
• Quizzes: \(0.15\)
• Midterm Exam: \(0.30\)
• Final Exam: \(0.35\)

The weighted average is calculated by multiplying each grade by its corresponding weight and summing the results: \[ \text{Course Grade} = (95 \times 0.20) + (78 \times 0.15) + (85 \times 0.30) + (90 \times 0.35) \]

\[ \begin{align_} 95 \times 0.20 &= 19.00 \\ 78 \times 0.15 &= 11.70 \\ 85 \times 0.30 &= 25.50 \\ 90 \times 0.35 &= 31.50 \\ \end{align_} \]

\[ \text{Course Grade} = 19.00 + 11.70 + 25.50 + 31.50 = 87.70 \]

Final Answer