Let's say I measure the length of a table to be 1.25 metres and the width to be 0.65 metres. Both measurements are accurate to the nearest cm.
Then the area of the table would be calculated as:
$$(1.25m)(0.65 m ) = 0.8125m^2$$
Standard practice is to give the final answer as $0.81 \pm 0.01m^2$ as that is the level of the accuracy of the given data.
Taking max values of: $$(1.255m)(0.655m ) = 0.822025m^2$$
and min values of $$(1.245m)(0.645m ) = 0.803025m^2$$
we get a result of $$0.812525 \pm 0.009500 m^2$$
My question is: Is there a probability distribution associated with the range $$0.812525 \pm 0.009500 m^2$$
I mean surely the chances of all values being max values or min values is much less than the chances of the values being nearer to the mean value.