1. **Problem statement:** A school has 740 students divided into 5 grades with given numbers. The principal wants to select a sample of 25 students maintaining the same proportion of grade 12 students as in the whole school. Calculate how many grade 12 students should be in the sample. 2. **Formula and explanation:** To find the number of students from grade 12 in the sample, use the proportion formula: $$\text{Number in sample from grade 12} = \frac{\text{Number of grade 12 students}}{\text{Total students}} \times \text{Sample size}$$ This ensures the sample reflects the population proportions. 3. **Calculation:** Number of grade 12 students = 181 Total students = 740 Sample size = 25 Calculate: $$\frac{181}{740} \times 25 = \frac{181 \times 25}{740} = \frac{4525}{740} \approx 6.11$$ Since the number of students must be whole, round to the nearest whole number: 6. 4. **Answer:** The sample should include **6** grade 12 students. --- 5. **Second question:** Identify the two sampling methods used when the principal selects students by asking those who took part in a previous survey and takes the first who reply positively up to the needed maximum. 6. **Explanation:** - This method is not random because it depends on who replies first. - It is not stratified because no proportional selection is done by strata in the selection process. - It is convenience sampling because the principal selects those who are easiest to reach (those who reply). - It is also quota sampling because the principal stops selecting once the required number is reached. 7. **Answer:** The two sampling methods are **Quota** and **Convenience**.