To determine the average number of students in the class who said they would benefit from tutoring, we can use the provided margin of error and the survey percentages.
Given:
- Lower margin: 10%
- Upper margin: 16%
- Margin of error: ±3%
- Total students surveyed: 8
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Calculate the Estimated Proportion: The estimated proportion who would benefit from tutoring can be taken as the midpoint between the lower and upper margins.
\[ \text{Estimated Proportion} = \frac{\text{Lower Margin} + \text{Upper Margin}}{2} = \frac{10% + 16%}{2} = \frac{26%}{2} = 13% \]
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Calculate Number of Students: Now, we will calculate the number of students out of 8 who would benefit from tutoring by multiplying the estimated proportion by the total number of students:
\[ \text{Number of Students} = \text{Estimated Proportion} \times \text{Total Students} = 0.13 \times 8 = 1.04 \]
Since we can't have a fraction of a student, we round this to the nearest whole number. Thus:
Approximately 1 student said they would benefit from tutoring, based on the midpoint estimate of the survey results.
However, let’s also check using the individual margins:
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For the lower margin (10% of 8 students): \[ \text{Lower estimate} = 0.10 \times 8 = 0.8 \quad \text{(approximately 1 student)} \]
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For the upper margin (16% of 8 students): \[ \text{Upper estimate} = 0.16 \times 8 = 1.28 \quad \text{(approximately 1 student)} \]
Both calculations confirm that the average number of students who said they would benefit from tutoring is approximately 1 student.