Behavior exhibited by humans and other organisms is generally inconsistent and biased and, thus, is often labeled irrational. However, the origins of this seemingly suboptimal behavior remain elusive. We developed a behavioral task and normative framework to reveal how organisms should allocate their limited processing resources such that sensory precision and its related metabolic investment are balanced to guarantee maximal utility. We found that mice act as rational inattentive agents by adaptively allocating their sensory resources in a way that maximizes reward consumption in previously unexperienced stimulus-reward association environments. Unexpectedly, perception of commonly occurring stimuli was relatively imprecise; however, this apparent statistical fallacy implies "awareness" and efficient adaptation to their neurocognitive limitations. Arousal systems carry reward distribution information of sensory signals, and distributional reinforcement learning mechanisms regulate sensory precision via top-down normalization. These findings reveal how organisms efficiently perceive and adapt to previously unexperienced environmental contexts within the constraints imposed by neurobiology.