Optimization of the strategy of passing the time-limited test according to the quantile criterion

The problem of constructing an optimal strategy for passing a time-limited test in the form of a stochastic programming problem with probabilistic constraints is considered. The strategy is a set of test tasks that maximizes the number of points scored for the test, the excess of which, while simultaneously fulfilling the limit on the time of the test, is guaranteed with a preselected confidence level, acting as a task parameter. The random parameters of the task are the user's response time to each test task and the correctness of the user's response to the task modeled by a random variable with a Bernoulli distribution. The resulting stochastic programming problem with probabilistic constraints is reduced to a deterministic integer mathematical programming problem. An algorithm to solve the initial problem is presented.