Question

A professor grades students on two tests, three quizzes, and a final  examination. Each test counts the same as three quizzes and the final  examination counts the same as two tests. Maegan has test scores of 87  and 96. Maegan’s quiz scores are 86, 72, and 83. Her final examination  score is 93. Use the weighted mean formula to find Maegan’s average  for the course. The professor rounds averages to the nearest integer. 

Answer 1

Let a quiz weight is a

Weight of test is 3a

Weight of the final examination $= 2 \times 3a = 6a$

Total weight of two tests, three quizzes of a final examination

$2(3a) +3a+ 6a = 1 \\ 6a +3a +6a = 1 \\ a = \frac{1}{15}$

Weighted average $\frac{\sum x_i \times w_i}{\sum w_i} = 89.9$