Respuesta :
The student's scores in his first three exams are 85, 78, and 81.
You have to find what score is needed on a fourth exam to have an average grade of at least 84 points.
To determine the average score of 4 exams, you have to add each score and divide it by the number of exams, following the formula:
[tex]\bar{X}=\frac{\sum ^n_1x_i}{n}[/tex]Where
xi represents each observation of the sample, in this exercise, it represents the score of each test.
n represents the same size, in this exercise, is the number of algebra tests
We know that:
The average is 84 points
n= 4 tests
Three observations are 85, 78, 81
If "x" represents the score of the fourth Test, then the calculation of the average grade can be expressed as:
[tex]84=\frac{85+78+81+x}{4}[/tex]From this expression, you can determine the value of x
-Solve the sum on the denominator:
[tex]84=\frac{244+x}{4}[/tex]-Multiply both sides by 4
[tex]\begin{gathered} 84\cdot4=4\cdot\frac{244+x}{4} \\ 336=244+x \end{gathered}[/tex]-Subtract 244 from both sides
[tex]\begin{gathered} 336-244=244-244+x \\ 92=x \end{gathered}[/tex]This means that the student needs at least 92 points on the fourth test, for his average score to be at least 84 points.
