1. **Problem Statement:** (a) Find the percentile rank for score 20 in the given set of 30 exam scores. (b) Find the percentile rank for score 68 in the same set. (c) Find Carmela's percent score given her marks and the total marks. 2. **Formula for Percentile Rank:** The percentile rank of a score $X$ is given by: $$\text{Percentile Rank} = \frac{\text{Number of scores less than } X}{\text{Total number of scores}} \times 100$$ 3. **Important Rule:** Always round up the percentile rank to the next whole number as instructed. --- ### Question 2 (a): Percentile rank for score 20 4. Count how many scores are less than 20. The scores less than 20 are: 18 (1 score). 5. Calculate percentile rank: $$\frac{1}{30} \times 100 = 3.33$$ 6. Round up: Percentile rank = 4 --- ### Question 2 (b): Percentile rank for score 68 7. Count how many scores are less than 68. Scores less than 68 are: 18, 23, 33, 38, 38, 38, 42, 51, 55, 56, 57, 63, 65, 66 (14 scores). 8. Calculate percentile rank: $$\frac{14}{30} \times 100 = 46.67$$ 9. Round up: Percentile rank = 47 --- ### Question 3 (a): Carmela's percent score 10. Use the formula for percent score: $$\text{Percent Score} = \frac{\text{Marks obtained}}{\text{Total marks}} \times 100$$ 11. Substitute values: $$\frac{618}{800} \times 100 = 77.25$$ 12. Carmela's percent score is 77.25 --- **Final answers:** - Percentile rank for score 20: 4 - Percentile rank for score 68: 47 - Carmela's percent score: 77.25