Questions: find the mean Score Percent of final grade Homework 88 10 Quiz 80 10 Quiz 93 10 Project 98 35 Final Exam 86 35

Solution Steps

To find the mean of the scores weighted by their respective percentages, we first calculate the weighted scores for each component:

\[ \text{Weighted Scores} = \begin{align_} \text{Homework} & : 88 \times \frac{10}{100} = 8.8 \\ \text{Quiz 1} & : 80 \times \frac{10}{100} = 8.0 \\ \text{Quiz 2} & : 93 \times \frac{10}{100} = 9.3 \\ \text{Project} & : 98 \times \frac{35}{100} = 34.3 \\ \text{Final Exam} & : 86 \times \frac{35}{100} = 30.1 \\ \end{align_} \]

Thus, the weighted scores are:

\[ \text{Weighted Scores} = [8.8, 8.0, 9.3, 34.3, 30.1] \]

Next, we calculate the mean \( \mu \) of the weighted scores using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

Where \( N \) is the number of scores. Here, we have:

\[ \sum_{i=1}^5 x_i = 8.8 + 8.0 + 9.3 + 34.3 + 30.1 = 90.5 \]

Thus, the mean is calculated as follows:

\[ \mu = \frac{90.5}{5} = 18.1 \]

Final Answer