## An Application Example
### Application
#### 3.2.1 Normality Test  
The assumption in the technique's basic tenet is that the normal distribution's sampling distribution may provide [25], i.e., the normal distribution's data samples are relevant to the \(N_{0}\) method. The distribution of the sample mean and the distribution of the sample variance are merged based on the properties of the normal distribution. The range of the sample mean under a certain level of confidence is computed using the principle of interval estimation. To demonstrate the applicability of this method, it is therefore important to conduct a normality test on the data of the study area prior to its application. H3 and H4 have 10 monolayers; the sandstone proportion of five wells was calculated, and its normality was tested in the working area as an example. Table 1 displays the information from the five wells. There are numerous ways to conduct a normality test; the most popular ones include the normal probability paper method, the Shapiro-Wilk test (S-W), the Kolmogorov-Smirnov test (K-S), and the skewness-kurtosis test. In this study, the distribution properties of samples were independently verified using the frequency histogram, Q-Q plot, P-P plot, skewness-kurtosis normality test and S-W normality test. The frequency histogram is a technique for determining if the sample data follows the normal distribution by comparing its similarity to the normal curve. While the Q-Q plot compares the degree of coincidence between the theoretical quantile and the sample quantile, the P-P plot compares the degree of coincidence between the cumulative frequency of the theoretical normal distribution and the cumulative frequency of the sample data. The datapoints essentially coincide with the theoretical curve if the sample data follows the normal distribution. Skewness and kurtosis use the symmetry and steepness of the data distribution to determine whether the normal distribution is obeyed. The S-W normality test method was employed to evaluate the hypothesis of the sample data since there were fewer than 50 samples [26]. The null hypothesis cannot be rejected when the test result is greater than the significance threshold, meaning that the samples follow the normal distribution. The next five findings of the five normality tests derived from data samples (Figure 3, Tables 2 and 3). The data distribution exhibits a normal pattern with a high frequency of intermediate values, as can be observed from the frequency histogram (Figure 3a). The findings of the P-P plot (Figure 3b) and the Q-Q plot (Figure 3c) demonstrate that the point data and theoretical line fit together nicely, and the data exhibits normal distributional properties. According to the comprehensive graph analysis (Figure 3), the data basically has the trend \begin{table}
\begin{tabular}{c c c c c c} \hline
**Wells** & **Well 1** & **Well 2** & **Well 3** & **Well 4** & **Well 5** \\ \hline Sandstone proportion (\%) & 88.928 & 83.415 & 87.766 & 75.550 & 95.971 \\ \hline \end{tabular}
\end{table} 
Table 1: Sandstone proportion data of 5 wells. of a normal distribution, but further analysis is needed to determine the conclusion. The results of the skewness and kurtosis tests were observed, and the statistical values of both were less than 1 (Table 2). In order to facilitate the analysis of the results, the Z-score was introduced here. The Z-score converts a certain original score value into a standard score value, which can make the previously uncomparable values comparable. When the significance level \(\alpha\) is 0.05, the absolute values of \(-\)0.383 and 0.341 are both smaller than 1.96 (Table 2), so it can be considered that the data basically follow the normal distribution. The data result for the S-W normality test table (Table 3) was 0.939, which was greater than the significance level of \(\alpha\) (\(\alpha\) = 0.05). It can be considered that the data has the characteristics of a normal distribution.