Odor cues from distant objects are sparse and highly fluctuating due to turbulent transport. However, whether animals can use these spatiotemporally varying statistics for decision-making is unclear. To address this question, we built a custom olfactometer to deliver discrete and brief (~40 ms halfwidth) odor pulses at arbitrary Poisson-distributed pulse rates. We then developed a behavioral task in which head-restrained, water-restricted mice had to make binary decisions based on the total odor pulse count in 5 seconds to obtain a water reward (Figures A-B). Performance in the task approached saturation when mice used total pulse counts far from the decision boundary to make decisions and degraded progressively when rate differences between the binary choices diminished (Figure C). Logistic regression of binary choices against the timing of odor pulses in the breathing cycle revealed that mice weighed sensory information differentially depending on the phase of the breathing cycle in which pulses arrived, a time dependency that correlated with the magnitude of activity in olfactory sensory neurons (Figure D). In vivo recordings from the Anterior Piriform Cortex (APCx) of trained animals revealed that odor pulse presentation triggered stochastic firing across neurons, with only a subpopulation showing dependency on pulse arrival time with respect to the respiratory phase (Figure E). Altogether, our study indicates that mice can integrate discrete, intermittent olfactory inputs over several seconds for decision-making, and that the arrival time of olfactory information with respect to breathing cycle modulates its representation across the olfactory pathway, as well as its perceptual weighing.