An insurance company runs three offices, A, B and C. The company’s employees are distributed as follows: 30% work in office A, 20% in office B and 50% in office C. In office A, 10% are managers, in office B, 20% are managers and in office C 5% are managers: (i) What is the total proportion of managers in the company?
Can someone clarify if I got the answer right?
Calculations for part i:
Office A: (0.30) x (0.10) = 0.03
Office B: (0.20) x (0.20) = 0.04
Office C: (0.20) x (0.05) = 0.01
= 0.08
This is what my teacher had? Is this right? Because Office C should be (0.50) x (0.05) = 0.025
Office A and B are fine. For Office C, it should be $0.5\cdot 0.05=0.025$. Thus, the proportion of managers is $0.03+0.04+0.025=0.095$.