Question

Sandra's Scores:What is the minimum score Sandra needs to make on the fifth test so that her mean test score is at least 85?

Answer 1

Given:

Sandra's scores on the first four tests:

`\text{ 87, 92, 76, 89}`

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:

`\text{ Average score = }\frac{\text{ Sum of all scores}}{\text{ Total number of subjects}}`

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,

`\text{ Average score = }\frac{\text{ Sum of all scores}}{\text{ Total number of subjects}}`
`\text{ 85 = }\frac{\text{ 87 + 92 + 76 + 89 + x}}{\text{ 5}}`
`\text{ 85 = }\frac{\text{ 344 + x}}{\text{ 5}}`
`\text{ (85)(5) = (}\frac{\text{ 344 + x}}{\text{ 5}})(5)`
`\text{ 425 = 344 + x}\rightarrow\text{ x + 344 = 425}`
`\text{ x = 425 - 344}`
`\text{ x = 81}`

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.