Question

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 92, the student scored 98. what is the student’s new weighted mean?
homework\t82\t5\t4.1
quiz\t78\t25\t19.5
project\t98\t15\t14.7
speech\t93\t20\t18.6
final exam\t92\t35\t32.2
\t\tweighted mean\t89.1
the student’s new weighted mean score is \boxed{}. (do not round.)

Explanation:

Step1: Find the difference in final exam score

The original final exam score was 92, and the new score is 98. The difference is \( 98 - 92 = 6 \).

Step2: Find the weight of the final exam

The weight of the final exam is 35% or 0.35.

Step3: Calculate the change in weighted score

The change in weighted score due to the final exam is \( 6\times0.35 = 2.1 \).

Step4: Add the change to the original weighted mean

The original weighted mean was 89.1. So the new weighted mean is \( 89.1+ 2.1=91.2 \).
Alternatively, we can recalculate the weighted score for the final exam and sum all weighted scores:

• New weighted score for final exam: \( 98\times0.35 = 34.3 \)
• Sum of other weighted scores: \( 4.1 + 19.5+14.7 + 18.6=56.9 \)
• New weighted mean: \( 56.9+34.3 = 91.2 \)

Answer:

91.2