The above theorems allow you to utilize the normal distribution to compute approximate probabilities for the variable X in the stated distributions. This is not always true for all distributions since some do not have parameters which allow for approaching normality. However, regardless of the distribution the Central Limit Theorem always allows you to approximate probabilities if they involve an average of repeated attempts...that is, for variable \(\overline{X}\text{.}\) This usefulness is illustrated in the examples below.