Respuesta :
Answer:
Between 64 and 86.5
Step-by-step explanation:
Let:
w=weight of the first three exams.
W=weight of the final exam.
Now, the sum of the weight of the four exams must be 100, besides we know that W=2w, hence:
[tex]w+w+w+W=100\\w+w+w+2w=100\\5w=100\\w=\frac{100}{5}=20[/tex]
So, each exam has a weight of 20% and the final exam would have a weight of 40%. Let's calculate the average score in order to get at leats 70:
Let:
x=Minimun score to earn a C
[tex]75*(\frac{20}{100} )+63*(\frac{20}{100} )+84*(\frac{20}{100} )+x*(\frac{40}{100} )=70[/tex]
Solving for x:
[tex]x=\frac{70-(44.4)}{0.4} =64[/tex]
Finally, let's calculate the average score in order to get 84:
Let:
y=Maximun score to earn a C:
[tex]75*(\frac{20}{100} )+63*(\frac{20}{100} )+84*(\frac{20}{100} )+y*(\frac{40}{100} )=79[/tex]
Solving for y:
[tex]y=\frac{79-(44.4)}{0.4} =86.5[/tex]
Using the mean concept, it is found that scores between 64 and 86.5 will result in him earning a grade of C.
What is the mean?
The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations.
In this problem:
- The observations are 75, 63, 84 and 2x, due to weight of the final test.
- Also due to the weight of the final test, there are 5 observations.
Hence, for a mean of 70:
[tex]70 = \frac{75 + 63 + 84 + 2x}{5}[/tex]
[tex]2x = 128[/tex]
[tex]x = \frac{128}{2}[/tex]
[tex]x = 64[/tex]
For a mean of 79, we have that:
[tex]79 = \frac{75 + 63 + 84 + 2x}{5}[/tex]
[tex]2x = 173[/tex]
[tex]x = \frac{173}{2}[/tex]
[tex]x = 86.5[/tex]
Scores between 64 and 86.5 will result in him earning a grade of C.
More can be learned about the mean concept at https://brainly.com/question/25639778
