GPA
A college course is graded based on one midterm and one final each worth 35% and 65% respectively. If a student scores a 30% on the midterm, what score (%) do they need on the final to pass with a 70% overall grade in the class?
Expand Hint
Weighted arithmetic mean:
$$$\bar{X}_{w}=\frac{\Sigma w_iX_i}{\Sigma w_i }$$$
where
$$X_i$$
is the value of the individual observation and
$$w_i$$
is the weight applied to
$$X_i$$
.
Hint 2
Solve for
$$X_{final}$$
:
$$$0.7=\frac{(0.35\times 30)+(0.65\times X_{final})}{35+65}$$$
Weighted arithmetic mean:
$$$\bar{X}_{w}=\frac{\Sigma w_iX_i}{\Sigma w_i }$$$
where
$$X_i$$
is the value of the individual observation and
$$w_i$$
is the weight applied to
$$X_i$$
.
$$$0.7=\frac{(0.35\times 30)+(0.65\times X_{final})}{35+65}$$$
$$$0.7(100)=10.5+(0.65\times X_{final})$$$
$$$X_{final}=\frac{(70-10.5)}{0.65}=\frac{59.5}{0.65}=91.54\%$$$
91.54%
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