The Cucker-Smale model for collective animal behavior is studied as a generalization. A system of delayed stochastic differential equations is used to formulate the model. It includes two other processes that are present in animal decision making but are sometimes overlooked in modeling: (i) individual behavior stochasticity, or flaws, and (ii) individual delayed responses to environmental cues. Using an appropriate Lyapunov functional, sufficient conditions for flocking for the generalized Cucker-Smale model are given. As a byproduct, one obtains a novel result concerning the delayed geometric Brownian motion's asymptotic nature. The paper's second section presents the findings from systematic numerical simulations. They not only show the analytical conclusions, but they also allude to a behavior of the system that is a little surprising—namely, that flocking might be made easier by adding an intermediate time delay.