- Identify the total city population as \(24,200\).
- Note that the proportion of residents in the Central region is \(0.44\).
- Multiply the total population by the proportion: \(24,200 \times 0.44 = 10,648\).
- Conclude that there are \(\boxed{10,648}\) residents living in the Central region.
Explanation
- Analyze the population data and proportions
To determine the number of residents living in the Central region, we analyze the provided data:
- The total population of the city is \(N = 24,200\).
- The probability distribution table indicates the proportion of residents in each region. Specifically, for the Central region, the probability \(P_{\text{Central}}\) is \(0.44\).
- Since these values represent proportions of the total population, we can find the number of residents in any specific region by multiplying the total population by the corresponding probability for that region.
- Calculate the number of residents in the Central region
The objective is to find the specific count of residents living in the Central region. We use the following relationship:
\[\text{Count}_{\text{Central}} = \text{Total Population} \times P_{\text{Central}}\]
Substituting the known values, we have:
\[\text{Count}_{\text{Central}} = 24,200 \times 0.44\]
Performing the multiplication:
\[24,200 \times 0.44 = 10,648\]
Thus, there are \(10,648\) residents living in the Central region.
Examples
This type of problem is very common in demographics and urban planning. For example, if a city planner knows the total population growth and the historical distribution of residents across different zones, they can use these proportions to forecast the number of people requiring services like water, electricity, or schools in specific areas of the city. Calculating \(\text{Population} \times \text{Proportion} = \text{Subgroup Count}\) is a foundational tool for data analysis in many fields.