What is the minimum score Jill needs on her next quiz to have a mean of at least 92?
Understand the Problem
The question is asking what score Jill needs on her next quiz in order to average at least a score of 92 across all her quizzes. This can be solved by calculating the total points needed to reach the average and then determining what score would allow that.
Answer
$90$
Answer for screen readers
Jill needs a minimum score of $90$ on her next quiz to average at least $92$.
Steps to Solve
- Calculate the Total of Current Scores
First, we find the total score of Jill's current quizzes.
Her scores are:
- 92
- 96
- 94
- 88
Thus, the total score is:
$$ \text{Total}_{\text{current}} = 92 + 96 + 94 + 88 = 370 $$
- Determine the Number of Quizzes
Jill has taken 4 quizzes so far, and with the next quiz, the total number will be:
$$ \text{Total quizzes} = 4 + 1 = 5 $$
- Calculate the Total Points Needed for the Desired Average
To find out how many total points are needed for an average of at least 92, we use the formula for average:
$$ \text{Average} = \frac{\text{Total points}}{\text{Number of quizzes}} $$
Rearranging gives:
$$ \text{Total points needed} = \text{Average} \times \text{Number of quizzes} $$
Substituting the values, we get:
$$ \text{Total points needed} = 92 \times 5 = 460 $$
- Calculate the Minimum Score Required on the Next Quiz
To find the minimum score Jill needs on her next quiz, we subtract her current total score from the total points needed:
$$ \text{Score needed} = \text{Total points needed} - \text{Total}_{\text{current}} $$
So:
$$ \text{Score needed} = 460 - 370 = 90 $$
Jill needs a minimum score of $90$ on her next quiz to average at least $92$.
More Information
In order to achieve an average, one must consider both the total scores and the number of quizzes. Maintaining a precise calculation is key to finding the right target score.
Tips
- Confusing the total needed for the average with just the sum of current scores.
- Forgetting to account for the additional quiz when calculating the new average.
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