Questions: A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and the final examination counts as two tests. Sara has test scores of 94,76 , and 72. Sara's quiz scores are 80,93,91, and 75 . Her final examination score is 94 . Use the weighted mean formula to find Sara's average for the course. (Round your answer to one decimal place.)

A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and the final examination counts as two tests. Sara has test scores of 94,76 , and 72. Sara's quiz scores are 80,93,91, and 75 . Her final examination score is 94 . Use the weighted mean formula to find Sara's average for the course. (Round your answer to one decimal place.)

Transcript text: A professor grades students on three tests, four quizzes, and a final examination. Each test counts as two quizzes and the final examination counts as two tests. Sara has test scores of 94,76 , and 72. Sara's quiz scores are 80,93,91, and 75 . Her final examination score is 94 . Use the weighted mean formula to find Sara's average for the course. (Round your answer to one decimal place.)

Solution

Solution Steps

To find Sara's average for the course using the weighted mean formula, we need to account for the weights of each component (tests, quizzes, and final examination). Each test counts as two quizzes, and the final examination counts as two tests. We will calculate the total weighted score and then divide it by the total weight.

Calculate the total score for tests, quizzes, and the final examination.
Assign weights to each component based on the given information.
Compute the weighted mean by dividing the total weighted score by the total weight.

Step 1: Calculate Total Weighted Score

The total weighted score is calculated by considering the contributions of tests, quizzes, and the final examination. The formula is:

\[ \text{Total Weighted Score} = \left( \sum \text{Test Scores} \times 2 \right) + \left( \sum \text{Quiz Scores} \times 1 \right) + \left( \text{Final Exam Score} \times 4 \right) \]

Substituting the values:

\[ \text{Total Weighted Score} = (94 + 76 + 72) \times 2 + (80 + 93 + 91 + 75) \times 1 + 94 \times 4 = 1199 \]

Step 2: Calculate Total Weight

The total weight is determined by the number of tests, quizzes, and the final examination, weighted accordingly:

\[ \text{Total Weight} = \left( \text{Number of Tests} \times 2 \right) + \left( \text{Number of Quizzes} \times 1 \right) + \left( \text{Final Exam Weight} \right) \]

Substituting the values:

\[ \text{Total Weight} = (3 \times 2) + (4 \times 1) + 4 = 14 \]

Step 3: Calculate Weighted Mean

The weighted mean is calculated by dividing the total weighted score by the total weight:

\[ \text{Weighted Mean} = \frac{\text{Total Weighted Score}}{\text{Total Weight}} = \frac{1199}{14} \approx 85.642857 \]

Rounding to one decimal place gives:

\[ \text{Weighted Mean} \approx 85.6 \]