Final answer:
The size of the labor force in the given country is 253 people, and the official unemployment rate is approximately 9.09%.
Step-by-step explanation:
To calculate the size of the labor force in the given country, we add the number of employed people and the number of unemployed people
Since the part-time workers looking for full-time jobs are already part of the workforce, we include them in the unemployed category.
Therefore, the labor force is the sum of people who are employed and the unemployed, which in this case is employs (500 - 120 - 150 = 230) + unemployed (23) = 253.
The official unemployment rate is calculated by dividing the number of unemployed people by the total labor force, then multiplying by 100 to get a percentage.
In this case, the unemployment rate is (23/253) * 100, which is approximately 9.09%.