The scores and their percents of the final grade for a statistics student are given. An error occurred grading the final exam. Instead of getting 86, the student scored 93. What is the​ student's new weighted​ mean? 

	Score	                Percent of Final Grade	           Weighted Score

Homework	 88	               5	                                         4.4

Quiz	       81	                        30	                                     24.3

Project	   97	                      20	                                   19.4

Speech	  91	                          10	                                    9.1

Final Exam	86	                           35	                               30.1



To calculate the student's new weighted mean after correcting the final exam score, we need to update the weighted score for the final exam and then recalculate the total weighted mean.

### Step 1: Update the Final Exam Weighted Score
The correct final exam score is 93. The percentage of the final grade that the final exam represents is 35%. 

The new weighted score for the final exam is calculated as:
\[
\text{New Weighted Score for Final Exam} = 93 \times \frac{35}{100} = 32.55
\]

### Step 2: Calculate the New Total Weighted Mean
Now, we sum the weighted scores with the updated final exam score.

\[
\text{New Total Weighted Mean} = 4.4 + 24.3 + 19.4 + 9.1 + 32.55
\]
\[
\text{New Total Weighted Mean} = 89.75
\]

Thus, the student's new weighted mean is **89.75**.

Would you like more details or have any questions? 

Here are five related questions to consider:
1. How would the weighted mean change if the project score were updated?
2. What if the homework score was adjusted to a different value?
3. How do you calculate the weighted mean if percentages don't add up to 100%?
4. Can the weighted mean be higher than the highest score?
5. How does a higher weight for the final exam impact the overall grade?

**Tip:** Always ensure that the sum of percentages in a weighted mean calculation equals 100% for accurate results.

Learn how to calculate the new weighted mean for a statistics student after correcting an error in the final exam score. Includes step-by-step calculations and adjustments for homework, quiz, project, speech, and final exam scores.

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