Question

We often deal with weighted​ means, in which different data values carry different weights in the calculation of the mean. For​ example, if the final exam counts for​ 50% of your final grade and 2 midterms each count for​ 25%, then you must assign weights of​ 50% and​ 25% to the final and​ midterms, respectively, before computing the mean score for the term. Apply the idea of weighted mean in the following exercise.
A student is taking an advanced anatomy class in which the midterm and final exams are worth 30% each and homework is worth 40% Of his final grade. On a 100-point scale, his midterm exam score was 82.5, his homework average score was 91.6, and his final exam score was 88.6.

Required:
a. On a 100-point scale, what is the student's overall average for the class?
b. The student was hoping to get an A in the class, which requires an overall score of 93.5 or higher. Could he have scored high enough on the final exam to get an A in the class?

Answer 1

Answer:

a) The student's overall average for the class is 87.97.

b) He would need a score above 100 to get an A, which means that he could not have scored high enough on the final exam to get an A in the class.

Step-by-step explanation:

Weighed average:

To solve this question, we find the student's weighed average, multiplying each of his grade by his weights.

Grades and weights:

Scored 82.5 on the midterm, worth 30%.

Scored 88.6 on the final exam, worth 30%.

Scored 91.6 on the homework, worth 40%.

a. On a 100-point scale, what is the student's overall average for the class?

Multiplying each grade by it's weight:

$A = 82.5*0.3 + 88.6*0.3 + 91.6*0.4 = 87.97$

The student's overall average for the class is 87.97.

b. The student was hoping to get an A in the class, which requires an overall score of 93.5 or higher. Could he have scored high enough on the final exam to get an A in the class?

Score of x on the final class, and verify that the average could be 93.5 or higher. So

$A = 82.5*0.3 + 88.6*0.3 + 0.4x$

$A \geq 93.5$

$82.5*0.3 + 88.6*0.3 + 0.4x \geq 93.5$

$0.4x \geq 93.5 - (82.5*0.3 + 88.6*0.3)$

$x \geq \frac{93.5 - (82.5*0.3 + 88.6*0.3)}{0.4}$

$x \geq 105.425$

He would need a score above 100 to get an A, which means that he could not have scored high enough on the final exam to get an A in the class.