Question

81. There are 500 people working in a company. The company's departments consist of production, marketing and finance. There are 250 people working in the production department, 150 people in the marketing department and 100 people in the finance department. When a sample is created using the stratified sampling method for 50 randomly selected people from the company, how many people will the sample consist of from each stratum?

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Answer to a math question 81. There are 500 people working in a company. The company's departments consist of production, marketing and finance. There are 250 people working in the production department, 150 people in the marketing department and 100 people in the finance department. When a sample is created using the stratified sampling method for 50 randomly selected people from the company, how many people will the sample consist of from each stratum?

Expert avatar
Jon
4.6
110 Answers
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

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