Given:
Sandra's scores on the first four tests:
[tex]\text{ 87, 92, 76, 89}[/tex]To have a mean score of at least 85 means that Sandra must have an average score of at least 85 on here 5 tests.
To get that, we will be using the following equation:
[tex]\text{ Average score = }\frac{\text{ Sum of all scores}}{\text{ Total number of subjects}}[/tex]Total number of subjects: 5
Our target mean (average) score: 85
Let,
x = the missing score needed to get a mean score of at least 85.
We get,
[tex]\text{ Average score = }\frac{\text{ Sum of all scores}}{\text{ Total number of subjects}}[/tex][tex]\text{ 85 = }\frac{\text{ 87 + 92 + 76 + 89 + x}}{\text{ 5}}[/tex][tex]\text{ 85 = }\frac{\text{ 344 + x}}{\text{ 5}}[/tex][tex]\text{ (85)(5) = (}\frac{\text{ 344 + x}}{\text{ 5}})(5)[/tex][tex]\text{ 425 = 344 + x}\rightarrow\text{ x + 344 = 425}[/tex][tex]\text{ x = 425 - 344}[/tex][tex]\text{ x = 81}[/tex]Therefore, for Sanda to get a mean test score of at least 85, she must get a minimum score of 81 on her fifth test.
The answer is 81.
