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.
