Question

a supervisor wants to know the average number of hours worked by employees in a factory. there are 18 managers, 240 laborers, and 54 administrators. three managers are chosen to participate in the survey. in order for the sample to accurately represent the population, about how many administrators should be chosen?
o 6
o 9
o 18
o 21

Explanation:

Step1: Set up proportion

Let $x$ be the number of administrators to be chosen. The ratio of managers chosen to total managers should equal the ratio of administrators chosen to total administrators. The ratio for managers is $\frac{3}{18}$, and for administrators is $\frac{x}{54}$. So we have the proportion $\frac{3}{18}=\frac{x}{54}$.

Step2: Cross - multiply and solve

Cross - multiplying gives $18x = 3\times54$. Then $18x=162$. Dividing both sides by 18, we get $x=\frac{162}{18}=9$.

Answer:

B. 9