To find out how many people the sample will consist of from each stratum, we need to determine the proportion of each department in relation to the total number of people.
Let:
- P_p be the proportion of people in the production department
- P_m be the proportion of people in the marketing department
- P_f be the proportion of people in the finance department
The proportion of each department is calculated as follows:
P_p = \frac{250}{500} = 0.5
P_m = \frac{150}{500} = 0.3
P_f = \frac{100}{500} = 0.2
Now, we will calculate the number of people in each stratum based on the proportions and the sample size:
- From the production department: 0.5 \times 50 = 25
- From the marketing department: 0.3 \times 50 = 15
- From the finance department: 0.2 \times 50 = 10
Therefore, the sample will consist of:
25 people from the production department
15 people from the marketing department
10 people from the finance department