Questions: A researcher wants to select a sample of 81 full-time employees who work in either the police, fire, or justice departments of Phoenix, Arizona, by performing stratified sampling. Of those three departments, 63% work in the police department, 30% work in the fire department, and 7% work in the justice department. How many full-time employees in each department should be surveyed? The study should include employees from the police department, employees from the fire department, and employees from the justice department. (Round to the nearest employee as needed.)

A researcher wants to select a sample of 81 full-time employees who work in either the police, fire, or justice departments of Phoenix, Arizona, by performing stratified sampling. Of those three departments, 63% work in the police department, 30% work in the fire department, and 7% work in the justice department. How many full-time employees in each department should be surveyed?

The study should include employees from the police department, employees from the fire department, and employees from the justice department. (Round to the nearest employee as needed.)

Transcript text: A researcher wants to select a sample of 81 full-time employees who work in either the police, fire, or justice departments of Phoenix, Arizona, by performing stratified sampling. Of those three departments, $63 \%$ work in the police department, $30 \%$ work in the fire department, and $7 \%$ work in the justice department. How many full-time employees in each department should be surveyed? The study should include $\square$ employees from the police department, $\square$ employees from the fire department, and $\square$ employees from the justice department. (Round to the nearest employee as needed.)

Solution

Solution Steps

To determine the number of employees to survey from each department, we will use the given percentages to calculate the proportion of the total sample size (81 employees) for each department. Multiply the total sample size by each department's percentage and round to the nearest whole number.

Step 1: Determine the Sample Size for Each Department

To find the number of employees to survey from each department, we multiply the total sample size by the percentage of employees in each department.

Step 2: Calculate the Number of Police Department Employees

The percentage of employees in the police department is $63\%$. Therefore, the number of police employees to survey is: \[ \text{Police Employees} = 81 \times 0.63 = 51 \]

Step 3: Calculate the Number of Fire Department Employees

The percentage of employees in the fire department is $30\%$. Therefore, the number of fire employees to survey is: \[ \text{Fire Employees} = 81 \times 0.30 = 24 \]

Step 4: Calculate the Number of Justice Department Employees

The percentage of employees in the justice department is $7\%$. Therefore, the number of justice employees to survey is: \[ \text{Justice Employees} = 81 \times 0.07 = 6 \]