Question

a students course grade is based on one midterm that counts as 10% of his final grade, one class - project that counts as 20% of his final grade, a set of homework assignments that counts as 40% of his final grade, and a final exam that counts as 30% of his final grade. his midterm score is 83, his project score is 82, his homework score is 84, and his final exam score is 81. what is his overall final score? his overall final score is (type an integer or a decimal. do not round.) what letter grade is he (a, b, c, d, or f)? assume that a mean of 90 or above is an a, a mean of at least 80 but less than 90 is a b, and so on.

Explanation:

Step1: Identify the weights and scores

The mid - term counts as 10% ($w_1 = 0.1$) with score $s_1=83$, the project counts as 20% ($w_2 = 0.2$) with score $s_2 = 82$, the homework counts as 15% ($w_3=0.15$) with score $s_3 = 84$, and the final exam counts as 30% ($w_4 = 0.3$) with score $s_4 = 81$. There is an unaccounted percentage of $1-(0.1 + 0.2+0.15 + 0.3)=0.25$. Assume the missing part has a score of 0 for simplicity (if not given otherwise).

Step2: Use the weighted - average formula

The weighted - average formula is $\bar{x}=\sum_{i = 1}^{n}w_is_i$. So, $\bar{x}=0.1\times83+0.2\times82 + 0.15\times84+0.3\times81+0.25\times0$.
First, calculate each product:
$0.1\times83 = 8.3$, $0.2\times82=16.4$, $0.15\times84 = 12.6$, $0.3\times81=24.3$, $0.25\times0 = 0$.
Then sum them up: $\bar{x}=8.3 + 16.4+12.6+24.3+0=61.6$.

Step3: Determine the letter grade

Since $61.6$ is less than 70, if we assume the grading scale: 90 - 100 is A, 80 - 89 is B, 70 - 79 is C, 60 - 69 is D, and below 60 is F, the letter grade is D.

Answer:

His overall final score is 61.6
His letter grade is D