Questions: The scores and their percent of the final grade for a statistics student are given. What is the student's weighted mean score? Score Percent of final grade Homework 82 15 Quiz 84 10 Quiz 93 10 Project 97 35 Final Exam 95 30 The student's weighted mean score is . (Simplify your answer. Round to two decimal places as needed.)

Solution Steps

The scores and their corresponding percentages of the final grade are defined as follows:

• Homework: \( 82 \) with a weight of \( 15 \)
• Quiz 1: \( 84 \) with a weight of \( 10 \)
• Quiz 2: \( 93 \) with a weight of \( 10 \)
• Project: \( 97 \) with a weight of \( 35 \)
• Final Exam: \( 95 \) with a weight of \( 30 \)

The weighted sum is calculated using the formula: \[ \text{Weighted Sum} = \sum_{i=1}^{n} \text{Score}_i \times \text{Weight}_i \] Substituting the values: \[ \text{Weighted Sum} = (82 \times 15) + (84 \times 10) + (93 \times 10) + (97 \times 35) + (95 \times 30) = 9245 \]

The total weight is the sum of all the weights: \[ \text{Total Weight} = 15 + 10 + 10 + 35 + 30 = 100 \]

The weighted mean score is calculated using the formula: \[ \text{Weighted Mean} = \frac{\text{Weighted Sum}}{\text{Total Weight}} = \frac{9245}{100} = 92.45 \]

The weighted mean score is rounded to two decimal places, resulting in: \[ \text{Weighted Mean (rounded)} = 92.45 \]

The student's weighted mean score is \( 92.45 \).

Final Answer