To determine the score a student needs on the fifth quiz to achieve an average (mean) score of 4 across five quizzes, follow these steps:
1. Calculate the desired total score:
- The desired mean score is 4.
- There are 5 quizzes in total.
- The total score needed to achieve a mean score of 4 can be found by multiplying the desired mean by the number of quizzes:
[tex]\[
\text{Total Required Score} = \text{Desired Mean} \times \text{Number of Quizzes} = 4 \times 5 = 20
\][/tex]
2. Sum the scores of the first four quizzes:
- The scores of the first four quizzes are 5, 4, 3, and 3.
- Calculate the sum of these scores:
[tex]\[
\text{Current Total Score} = 5 + 4 + 3 + 3 = 15
\][/tex]
3. Determine the score needed on the fifth quiz:
- To find the score needed on the fifth quiz, subtract the sum of the first four quiz scores from the total required score:
[tex]\[
\text{Required Score Fifth Quiz} = \text{Total Required Score} - \text{Current Total Score} = 20 - 15 = 5
\][/tex]
Therefore, the student needs to score 5 on the fifth quiz to achieve a mean score of 4 across all five quizzes.
