Human decision-making often occurs under conditions of uncertainty, where understanding probabilities is essential for making informed choices. This study investigates how people perceive and apply probabilistic information in various decision-making contexts. A combination of quantitative and qualitative methods was used to analyze the decision patterns of 200 individuals from diverse backgrounds through scenarios involving uncertainty. The results show that most participants prefer relying on intuition or personal experience rather than using statistical reasoning. Several cognitive biases, such as ignoring probability, overestimating confidence, and relying on readily available information, were commonly observed. However, participants with a stronger grasp of probability concepts demonstrated more logical and beneficial decision-making, particularly in financial and organizational settings. The study highlights a clear link between probability literacy and decision quality. Improving public understanding of probabilistic thinking could enhance decision outcomes, especially in situations involving risk. Educational efforts to integrate probability awareness into learning environments are recommended to support better decision-making both individually and collectively.

Rainfall potential analysis plays a critical role in the management of air resources, mitigation of hydrometeorological disasters, and agricultural activity planning. Accurate estimation of rainfall patterns is essential to ensure effective decision-making in irrigation systems, water resource management, and disaster risk reduction strategies. This study aims to model the probability of rainfall occurrence using a statistical approach based on historical data obtained from the Bureau of Meteorology. The data spans a multi-year period and captures seasonal and regional variability in rainfall events. To characterize rainfall patterns, various probability distributions are tested, including the exponential distribution and the Weibull distribution, which are commonly applied in hydrological studies. Furthermore, the Markov chain method is employed to assess the likelihood of rainfall occurrence on a given day based on the conditions of the preceding day, thereby capturing temporal dependencies. Parameter estimation is conducted using Maximum Likelihood Estimation (MLE), a robust statistical method that enhances the precision of the model. The suitability of each probability distribution in representing the observed rainfall data is evaluated through goodness-of-fit tests such as the Kolmogorov-Smirnov test. The findings reveal that certain distributions align more closely with the local rainfall characteristics, demonstrating the importance of regional analysis in climate modeling. The combination of probabilistic modeling, Markov analysis, and rigorous statistical testing provides a reliable framework for forecasting rainfall. These results are expected to serve as a scientific basis for stakeholders in agriculture, environmental planning, and disaster preparedness, offering insights that support sustainable water resource utilization and risk management.

This study explores the application of the normal distribution in analyzing the height data of Mathematics Education students at FMIPA Universitas Negeri Medan in 2024. Employing a quantitative descriptive-analytic methodology, the research involved collecting primary data from 10 randomly selected students through a questionnaire-based survey. Descriptive statistical analysis revealed a mean height of 161.4 cm with a standard deviation of 8.79 cm. The median height was found to be 164 cm, while the mode was 150 cm, indicating a slightly skewed distribution. To assess the suitability of the normal distribution model, the Shapiro-Wilk test was applied, resulting in a W value of 0.921 and a p-value of 0.361, which exceeds the 0.05 significance level. This confirms that the sample data follow a normal distribution pattern. The findings were further supported through visual representation using histograms and analysis based on the empirical rule, which showed that approximately 68% of the students' heights fall within one standard deviation of the mean (152.81–169.99 cm). Additionally, probability calculations demonstrated that the likelihood of a student being 160 cm tall or shorter is approximately 43.64%. These results validate the effectiveness of the normal distribution as a tool for analyzing biological or physical characteristics, even in small sample sizes. However, the study acknowledges its limitation in terms of sample size and suggests that future research involve larger and more diverse populations to enhance generalizability. The study highlights the relevance of normal distribution in statistical modeling, particularly for educational and health-related data interpretation and decision-making processes.