False.
The definition of Arbitrary and Capricious is:
A clear error of judgment; an action not based upon consideration of relevant factors and so is arbitrary, capricious, an abuse of discretion or otherwise not in accordance with law or if it was taken without observance of procedure required by law. 5 USC. 706(2)(A) (1988).
What is arbitrary to one can be perfectly sane to another one hence the statement is false.