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Calculating the probabilities can be aided by creating a visual, like the one in Figure 11. For those distributions that are normal but not standard normal, the random variable X can be standardized by  .
But how can one discover the approximate underlying distribution of the data set [2]? 
Figure 11. Normal Curve Probabilities [5] DETERMINING UNDERLYING DISTRIBUTIONS In order to provide some insight into the underlying distribution of a data set, Karl Pearson suggested a method using the chi-square statistic and hypothesis testing, which tests the suitability of a probabilistic model [3]. The chi-square goodness-of-fit test can determine whether the underlying distribution is what is assumed in the null hypothesis, or whether it is another distribution [2]. HYPOTHESIS TESTING AND SIGNIFICANCE LEVELS From prior studies, a hypothesis is simply an educated guess in regards to the problem statement. With this in mind, we start by creating a null hypothesis, denoted  . The null hypothesis is the initial assumption of one parameter in the sample set. The alternative hypothesis, , is an assertion that is a contradiction of . Based on a specified significance level, , one either rejects the null hypothesis or fails to reject the null hypothesis [2].
Once the null and alternative hypotheses are determined, a test-statistic is calculated from the distribution. If the test-statistic falls in the critical region, then you reject the null hypothesis [3]. The critical regions are defined in the Tables 2 and 3. If the null hypothesis is not accepted, one cannot assume that the alternative hypothesis is true.
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