Within +/- 2.33 sec per 24hr of continued operation, what would +/- be for 5hrs?

Question

A stop watch was found to be accurate to w/ in 2.33 seconds per 24hr of continuous operation, what would the accuracy be for 5hrs of operation?

Answer 1

It depends on the cause of the inaccuracy. There are 3 different types of errors that could create inaccuracy: 1) precision error - this is usually half of the divisions of the measuring device. For example, a stopwatch that measures to the nearest second has a precision error of +/- 0.5 seconds. A stopwatch that measures to the nearest tenth of a second has a precision error of +/- 0.05 seconds. The precision error for the particular device will always be the same, no matter if you measure 1 second, 1 minute, 1 hour, 5 hours, or 24 hours. 2) random errors - these errors will be different each time you make a measurement. Human measuring inaccuracy usually is random. For example, the inaccuracy of starting the stopwatch and stopping the stopwatch when timing a race would be a random error. Again, these random errors will probably be about the same regardless of whether you are timing a 1 minute event, a 1 hour event, a 5 hour event, or a 24 hour event. 3) systematic errors - these are errors caused by the device or the measurement procedure, and are not random. These errors may be either proportional to the quantity being measured, or they may be constant. Example: an old analog spring bathroom scale that is not "zeroed" may be exactly 2 pounds off (in which case the error will not change regardless of how much weight is being measured) or the scale's spring may be calibrated wrong, in which case the error will be proportional to the weight placed on it.

Without knowing the type of error that contributes to the +/- 2.33 second inaccuracy over 24 hours, one really cannot say if the stopwatch would also be inaccurate by +/- 2.33 seconds when measuring 5 hours (for example, if it were a random error) or if the stopwatch would be inaccurate by 5/24 of +/- 2.33 seconds (for example, a systematic error that increased with the measured quantity).

Answer 2

basic ratio and proportion.....

2.33 x 5 / 24 = 0.48541666666666666666666667

Answer 3

0.48542