This paper considers Capacitated Vehicle Routing Problem(CVRP) in an imprecise and random environment. The deterministic version of the problem deals with finding a set of routes in such a way that the demand of all the customers present in the network are satisfied and the cost incurred in performing these operations comes out to be a minimum. In practical life situations, problems are not always defined in crisp form. Phenomenons like randomness and impreciseness are quite natural to arise in real life. This work presents CVRP in such a mixed environment. In this work, the demands of the customers are assumed to be stochastic in nature and are revealed only upon the arrival of the salesman. Moreover, the edge weights are representing the time required to traverse the edge and hence are both imprecise and random in nature. Different traffic conditions, weather conditions and many other factors corresponds to the random nature of edge weights and varying speed of the vehicle corresponds to the impreciseness. Thus, in this work, edge weights are represented by discrete fuzzy random variables. In this paper, an expectation based approach has been used to deal with randomness. A procedure based on Branch and Bound algorithm has been used to find routes with minimum cost. A numerical example has also been presented to explain the working of the method proposed.