Question

In a class in which the final course grade depends entirely on the average of four equally weighted 100-point tests, Erica has scored 86, 79, and 85 on the first three. What range of scores on the fourth test will give Erica a C for the semester (an average between 70 and 79, inclusive)? Assume that all test scores have a non-negative value.

Answer 1

Erica must score between 30 and 66 to obtain a grade average of C.

Explanation:

We are given the following ion the question:

Erica's score:

86, 79, and 85

To get a grade C, the average score of Erica must lie between 70 and 79.

Formula:

`Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}`

Let x be the score on fourth test.

Thus, we can write:

`70\leq (86+79+85+x)/(4)\leq 79\\\\280\leq 250+x\leq 316\\280-250\leq x \leq 316-250\\30\leq x\leq 66`

Thus, Erica must score between 30 and 66 to obtain a grade average of C.