In this chapter, we explored the concepts of random variables and their associated probability distributions. We began by classifying random variables into discrete and continuous types. For discrete random variables, which have a finite or countable set of outcomes, we delved into distributions such as the uniform, binomial, and Poisson. In contrast, for continuous random variables, which possess an infinite set of possible outcomes within a given range, we examined the normal distribution in detail. We concluded the chapter with a deep dive into the significance of the Z-score and the utility of the Z-table, highlighting their crucial roles in understanding and interpreting the normal distribution. Through this chapter, we provided a comprehensive mathematical framework for structuring and understanding the intricate world of randomness.