A group of students was asked about favorite colors, and 20% of the students said that their favorite color is red.  There are about 3000 students in the school.  If the margin of error is +2%, what is the range of number  of students who likely say their favorite color is red?

To determine the range of the number of students who likely say their favorite color is red, given a margin of error, follow these steps:

1. **Calculate the percentage range**:
   - The given percentage of students who said red is 20%.
   - The margin of error is ±2%.
   - Therefore, the range of percentages is from \( 20\% - 2\% = 18\% \) to \( 20\% + 2\% = 22\% \).

2. **Find the number of students**:
   - The total number of students in the school is approximately 3000.
   - Calculate the number of students corresponding to the lower and upper bounds of the percentage range:

   \[
   \text{Lower bound} = 18\% \times 3000 = 0.18 \times 3000 = 540
   \]

   \[
   \text{Upper bound} = 22\% \times 3000 = 0.22 \times 3000 = 660
   \]

3. **Conclusion**:
   The range of the number of students who likely say their favorite color is red is between **540 and 660** students.

Would you like more details or have any questions?

Here are 5 related questions:
1. How does the margin of error affect survey results?
2. How would the range change if the margin of error was ±1%?
3. How do you calculate percentage increase or decrease?
4. What factors influence the margin of error in surveys?
5. What is the importance of sample size in survey accuracy?

**Tip:** To reduce the margin of error, increasing the sample size typically helps make survey results more accurate.

A group of students was asked about favorite colors, and 20% of the students said that their favorite color is red. There are about 3000 students in the school. If the margin of error is +2%, what is the range of number of students who likely say their favorite color is red?

Calculate the estimated range of students who likely say their favorite color is red, given a 20% preference and a 2% margin of error in a school of 3000 students. Learn how to apply percentages and margin of error to make accurate estimates. Suitable for Grades 6-8 students.

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