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Statistics is a branch of mathematics focused on gathering, analyzing, interpreting, and presenting data. In the exercise, statistics help us understand the likelihood of a person being under correctional supervision. This is done through probability, which is a measure of how likely an event is to occur.

In statistics, probability is calculated by dividing the number of successful outcomes by the total number of possible outcomes. In our case, the successful outcome is choosing a person under correctional supervision. The total number of possible outcomes is the entire adult population in this state. By performing this division, we obtain a probability of 0.092. This number tells us that there is a 9.2% chance of randomly selecting an individual from the population who is under correctional supervision.

Key concepts like variance and standard deviation aren't necessary here, but they can play significant roles in more complex probability problems, ensuring deeper understanding of data distribution and its implications.

Applied mathematics involves using mathematical methods and models to solve practical problems. This exercise demonstrates applied mathematics through the calculation of probability, a mathematical concept.

In real-world scenarios, like assessing correctional supervision, applied mathematics helps quantify conditions that may influence policy or resource allocation. Here, applied mathematical methods are seen when we find the probability that a person is under correctional supervision by dividing the observed frequency (people under supervision) by the total population.

This simple application shows how refined mathematical techniques can offer measurable insights into societal issues. The use of probabilities as seen here aids in planning and decision-making, revealing the power of mathematics in practical applications.

Problem-solving in mathematics is a crucial skill that involves identifying, analyzing, and solving mathematical problems. The exercise demonstrates several essential steps:

• Identifying given information (population and number under supervision)
• Using relevant formulae (probability formula).
• Substituting and simplifying to reach a solution.

By systematically breaking down the problem, we arrive at an answer that has real-world implications.

Complex problems require solid understanding and skills in simplification and substitution. It's about more than just arriving at the solution; it's also ensuring that the correct logic and method are applied. The solution highlights a straightforward sequence.
Using this step-by-step approach optimizes the process of finding accurate solutions and ensures that similar future problems can be tackled with confidence.