So, if the \(\chi^2\) distribution is based upon the gamma distribution, why might one want to save it for this point in time? The Gamma distribution has a specific setup for the random variable for solving a particular problem...finding the probability that it takes an amount of time in order to reach a defined number of successes. \(\chi^2\) simply is created by using a redesign of the gamma formula but with no particular problem to solve in mind. However, \(\chi^2\) has a number of properties that are useful for making inferences from sample data as you will see later. The theorem below shows an important relationship between the \(\chi^2\) distribution and the standard normal distribution.