To determine the appropriate unemployment rate for the entire region of northwest Ohio, we will follow these steps: calculate the number of unemployed people in each county, find the total number of unemployed people in the region, find the total labor force in the region, and then use these values to calculate the overall unemployment rate. We'll round the final result to 2 decimal places.
### Step-by-Step Solution
1. Calculate the number of unemployed people in each county:
- Wood County:
- Unemployment Rate: 4.5%
- Workforce: 15,300
- Number of unemployed people:
[tex]\[
\frac{4.5}{100} \times 15300 = 688.5
\][/tex]
- Ottawa County:
- Unemployment Rate: 3.0%
- Workforce: 10,400
- Number of unemployed people:
[tex]\[
\frac{3.0}{100} \times 10400 = 312.0
\][/tex]
- Lucas County:
- Unemployment Rate: 10.2%
- Workforce: 150,600
- Number of unemployed people:
[tex]\[
\frac{10.2}{100} \times 150600 = 15361.2
\][/tex]
2. Calculate the total number of unemployed people in the region:
[tex]\[
\text{Total Unemployed} = 688.5 + 312 + 15361.2 = 16361.7
\][/tex]
3. Calculate the total workforce in the region:
[tex]\[
\text{Total Workforce} = 15300 + 10400 + 150600 = 176300
\][/tex]
4. Calculate the overall unemployment rate:
[tex]\[
\text{Overall Unemployment Rate} = \left( \frac{16361.7}{176300} \right) \times 100
\][/tex]
Simplifying:
[tex]\[
\frac{16361.7}{176300} \approx 0.0928
\][/tex]
[tex]\[
0.0928 \times 100 = 9.28\%
\][/tex]
Therefore, the appropriate unemployment rate for the entire region of northwest Ohio is 9.28%.
