Final answer:
To determine precision and accuracy of measurements, we need to understand how close they are to each other and to the true value respectively. However, without additional context, we cannot assess accuracy, and thus the best answer is that the measurements are both imprecise and inaccurate. The uncertainty of the new stopwatch means that slight differences in sprint times cannot be conclusively compared.
Step-by-step explanation:
In the context of this question, precision refers to how close multiple measurements are to each other, while accuracy refers to how close a measurement is to the true or accepted value. For the times given (4.01 seconds, 40 seconds, and 420.1 seconds), we would need more context to determine their precision and accuracy, such as the true time we are trying to measure or a set of repeated measurements. However, if we assume these times are individual measurements and they should all be exactly the same, then the measurements are imprecise because they are significantly different from each other. Without additional context, we cannot conclude their accuracy. Therefore, the best answer from the provided information is Imprecise and inaccurate (D).
When assessing reproducibility, precise values that are consistently repeated under the same conditions suggest a high level of control over the variables in the experiment. Hence, precise values are generally more reproducible than imprecise ones.
Concerning the new stopwatch with an uncertainty of ±0.05 s, the different times recorded for the sprinter on separate occasions (12.04 seconds and 11.96 seconds) suggest there was an improvement; however, the uncertainty means that these two times could be seen as equivalent. Therefore, while the times suggest the runner was faster in the second sprint, the uncertainty means this cannot be concluded with certainty. In cases where the differences in time are smaller than the uncertainty, it can be difficult to definitively conclude which time was faster.