Answer :
To determine what score Anna needs on her fifth quiz to have an average (mean) score of 85, we'll follow these steps:
1. Determine the target mean score and the number of quizzes:
- Target mean score = 85
- Total number of quizzes = 5
2. Calculate the total score needed for five quizzes to achieve the target mean:
- Mean score is calculated as (total score)/(number of quizzes)
- We need:
[tex]\[ \text{total score} = \text{mean} \times \text{number of quizzes} \][/tex]
- Substituting the values:
[tex]\[ \text{total score} = 85 \times 5 = 425 \][/tex]
3. Find the sum of Anna's scores on the first four quizzes:
- The scores are 78, 86, 90, and 82
- Total score for the first four quizzes:
[tex]\[ 78 + 86 + 90 + 82 = 336 \][/tex]
4. Calculate the required score on the fifth quiz:
- Total score needed = 425
- Current total score = 336
- Therefore, the score needed on the fifth quiz:
[tex]\[ \text{required score} = \text{total target score} - \text{current total score} \][/tex]
- Substituting the values:
[tex]\[ \text{required score} = 425 - 336 = 89 \][/tex]
So, Anna needs to score 89 on her fifth quiz to have an average score of 85. Therefore, the correct answer is 89.
1. Determine the target mean score and the number of quizzes:
- Target mean score = 85
- Total number of quizzes = 5
2. Calculate the total score needed for five quizzes to achieve the target mean:
- Mean score is calculated as (total score)/(number of quizzes)
- We need:
[tex]\[ \text{total score} = \text{mean} \times \text{number of quizzes} \][/tex]
- Substituting the values:
[tex]\[ \text{total score} = 85 \times 5 = 425 \][/tex]
3. Find the sum of Anna's scores on the first four quizzes:
- The scores are 78, 86, 90, and 82
- Total score for the first four quizzes:
[tex]\[ 78 + 86 + 90 + 82 = 336 \][/tex]
4. Calculate the required score on the fifth quiz:
- Total score needed = 425
- Current total score = 336
- Therefore, the score needed on the fifth quiz:
[tex]\[ \text{required score} = \text{total target score} - \text{current total score} \][/tex]
- Substituting the values:
[tex]\[ \text{required score} = 425 - 336 = 89 \][/tex]
So, Anna needs to score 89 on her fifth quiz to have an average score of 85. Therefore, the correct answer is 89.
