To determine if the company's claim was correct, we need to verify whether the actual result falls within a range that is [tex]\( \pm 3 \% \)[/tex] of the predicted value. Let's follow the steps to calculate this:
1. Identify the prediction and the result:
- Prediction: [tex]\( 3400 \)[/tex] votes
- Result: [tex]\( 3300 \)[/tex] votes
2. Calculate the deviation percentage:
- The company's claim states that the prediction will be within [tex]\( \pm 3 \% \)[/tex] of the result.
3. Compute the allowed deviation:
- Deviation percentage as a decimal: [tex]\( 3\% = 0.03 \)[/tex]
- Allowed deviation = [tex]\( 3400 \times 0.03 = 102 \)[/tex] votes
4. Determine the acceptable range (bounds) for the prediction:
- Lower bound = Prediction - Allowed deviation = [tex]\( 3400 - 102 = 3298 \)[/tex] votes
- Upper bound = Prediction + Allowed deviation = [tex]\( 3400 + 102 = 3502 \)[/tex] votes
5. Check if the actual result is within the allowed range:
- Lower bound: [tex]\( 3298 \)[/tex] votes
- Upper bound: [tex]\( 3502 \)[/tex] votes
- Actual result: [tex]\( 3300 \)[/tex] votes
6. Conclusion:
- Since [tex]\( 3300 \)[/tex] votes (the actual result) falls within the range [tex]\( 3298 \)[/tex] to [tex]\( 3502 \)[/tex], the company's prediction is indeed within the [tex]\( \pm 3 \% \)[/tex] deviation. Therefore, the company's claim was correct.
