Question

a professor grades students on four tests, a term paper, and a final examination. each test counts as 15% of the course grade. the term paper counts as 20% of the course grade. the final examination counts as 20% of the course grade. alan has test scores of 84, 92, 82, and 78. alan received an 84 on his term paper. his final examination score was 90. use the weighted mean formula to find alans average for the course. (round your answer to one decimal place.)

Explanation:

Step1: Calculate test average

First, find the mean of Alan's test scores:
$\text{Test Average} = \frac{84 + 92 + 82 + 78}{4} = \frac{336}{4} = 84$

Step2: Assign weights to each component

Define the weighted values for each grade component:

• Tests: $84 \times 0.15 \times 4 = 84 \times 0.6$
• Term paper: $84 \times 0.20$
• Final exam: $90 \times 0.20$

Step3: Compute weighted sum

Calculate each weighted term and sum them:
$\text{Weighted Sum} = (84 \times 0.6) + (84 \times 0.20) + (90 \times 0.20)$
$\text{Weighted Sum} = 50.4 + 16.8 + 18$

Step4: Total the weighted values

Add the results from Step3:
$\text{Weighted Sum} = 50.4 + 16.8 + 18 = 85.2$

Answer:

85.2