This paper investigates the trade-off between throughput and peak age of information (PAoI) outage probability in a multi-sensor information collection system. Each sensor monitors a physical process, periodically samples its status, and transmits the updates to a central access point over a shared radio resource. The trade-off arises from the interplay between each sensor's sampling frequency and the allocation of the shared resource. To optimize this trade-off, we formulate a joint optimization problem for each sensor's sampling delay and resource allocation, aiming to minimize a weighted sum of sampling delay costs (representing a weighted sum of throughput) while satisfying PAoI outage probability exponent constraints. We derive an optimal solution and particularly propose a closed-form approximation for large-scale systems. This approximation provides an explicit expression for an approximately optimal trade-off, laying a foundation for designing resource-constrained systems in applications that demand frequent updates and also stringent statistical timeliness guarantees.