Computing with words provides symbolic and semantic methodology to deal with imprecise information associated with natural languages. It encapsulates various fuzzy logic techniques developed in past decades and formalizes them. Z-number is an emerging paradigm that has been utilized in computing with words among others. The concept of a Z-number is intended to provide a basis for computation with numbers, specifically with reliability of information. Z-numbers are in confluence between the two most prominent approaches to uncertainty, probability and possibility, that allow computations on complex statements. Certain computations related to Z-numbers are ambiguous and complicated leading to its slow adaptation into areas such as computing with words. The biggest contributing factor to the complexity is the usage of probability distributions in the computations. This paper seeks to provide an applied model of Z-number based on certain realistic assumptions regarding probability distributions. Algorithms are presented to implement this model and integrate it into an expert system shell for computing with words called CWShell. CWShell is a software tool that abstracts the underlying computation required for computing with words, and provides a convenient way to represent and compute with unstructured natural language using specialized language called Generalized constraint language (GCL). This paper introduces new constructs for Z-numbers to GCL and provides detailed inference mechanism and computation strategy on those constructs. We present two case studies to demonstrate the working and feasibility of the approach.