Computing with words (CW) provides symbolic and semantic methodology to deal with imprecise information associated with natural language. The CW paradigm rooted in fuzzy logic, when coupled with an expert system, offers a general methodology for computation with fuzzy variables and a fusion of natural language propositions for this purpose. Fuzzy variables encode the semantic knowledge, and hence, the system can understand the meaning of the symbols. The use of words not only simplifies the knowledge acquisition process, but can also eliminate the need of a human knowledge engineer. CW 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 other constructs. The concept of Z-number is intended to provide a basis for computation with numbers that deals with reliability and likelihood. Z-numbers are confluence of 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 their slow adaptation into areas such as computing with words. Moreover, as acknowledged by Zadeh, there does not exist a unique solution to these problems. The biggest contributing factor to the complexity is the use of probability distributions in the computations. This dissertation seeks to provide an applied model of Z-number based on certain realistic assumptions regarding the 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 reason on a unstructured natural language.