Final Answer:
(a) The lower bound for the time t is 26.5 seconds.
(b) The upper bound for the time t is 27.5 seconds.
(c) The error interval is [26.5 seconds, 27.5 seconds].
Explanation:
In rounding to the nearest second, the value is rounded to the nearest whole number. For the given time t, which is 27 seconds correct to the nearest second, the lower bound would be halfway between 26 seconds and 27 seconds, as rounding down would result in 26 seconds. Therefore, the lower bound is 26.5 seconds.
Conversely, the upper bound is halfway between 27 seconds and 28 seconds, as rounding up would result in 28 seconds. Thus, the upper bound is 27.5 seconds. The error interval, then, is the range between the lower and upper bounds, denoted as [26.5 seconds, 27.5 seconds].
To summarize, when dealing with measurements rounded to the nearest second, understanding the rounding process is crucial. The lower and upper bounds are determined by considering the midpoint between the adjacent whole numbers. In this case, the error interval provides a range within which the true value is likely to lie, acknowledging the inherent uncertainty introduced by rounding.