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?
6
9
18
21

Explanation:

Step1: Calculate the proportion of managers in the population

The total number of employees is \(240 + 54+18=312\). The proportion of managers is \(\frac{18}{312}\).

Step2: Use the proportion to find the number of administrators in the sample

Since 3 managers are chosen, let the number of administrators be \(x\). We set up a proportion \(\frac{3}{18}=\frac{x}{54}\) (because the ratio of the sample - to - population should be the same for each group). Cross - multiply gives \(18x = 3\times54\).

Step3: Solve for \(x\)

\(18x=162\), then \(x = 9\).

Answer:

9