Final answer:
The error interval for the weight of a suitcase rounded to the nearest kilogram is from 24.5 kg to below 25.5 kg. To calculate percent uncertainty, divide the uncertainty by the average weight and multiply by 100%. Using an example with an average weight of 5.1 lb and uncertainty of 0.3 lb, the percent uncertainty is approximately 5.9%.
Step-by-step explanation:
Error Interval for the Weight of a Suitcase
The question refers to finding the error interval for the weight of one suitcase, given that the weight is 25 kg correct to the nearest kilogram. The error interval for the weight is determined by considering the rounding to the nearest kilogram. Since the suitcase weight is rounded to 25 kg, the lower bound of the weight would be just below 24.5 kg—since any value less than that would round down to 24 kg. Conversely, the upper bound would be just below 25.5 kg—since any value 25.5 kg or above would round up to 26 kg. Therefore, the error interval is 24.5 kg to below 25.5 kg.
Calculating Percent Uncertainty
To calculate the percent uncertainty, we divide the uncertainty by the average weight and then multiply by 100%. If we take an example where a bag's average weight is 5.1 lb and the uncertainty is 0.3 lb, the percent uncertainty is calculated as follows:
- Divide the uncertainty (0.3 lb) by the average weight (5.1 lb): 0.3 lb / 5.1 lb = 0.0588.
- Multiply by 100% to get the percent uncertainty: 0.0588 * 100% = 5.88%, which can be rounded to 5.9%.