1. **Problem statement:** We have a set of 30 exam scores and need to find the percentile ranks for scores 20 and 68. 2. **Formula for percentile rank:** $$\text{Percentile Rank} = \frac{\text{Number of scores less than the given score} + 0.5 \times \text{Number of scores equal to the given score}}{\text{Total number of scores}} \times 100$$ 3. **Step (a): Percentile rank for score 20** - Count scores less than 20: The scores less than 20 are 18 only, so count = 1. - Count scores equal to 20: There are none, so count = 0. - Total scores = 30. Calculate: $$\text{Percentile Rank} = \frac{1 + 0.5 \times 0}{30} \times 100 = \frac{1}{30} \times 100 = 3.33$$ Round up to next whole number: $$4$$ 4. **Step (b): Percentile rank for score 68** - Count scores less than 68: Scores less than 68 are all scores below 68. From the list, these are 18, 23, 33, 38, 38, 38, 42, 51, 55, 56, 57, 63, 65, 66 (14 scores). - Count scores equal to 68: There are 4 scores equal to 68. - Total scores = 30. Calculate: $$\text{Percentile Rank} = \frac{14 + 0.5 \times 4}{30} \times 100 = \frac{14 + 2}{30} \times 100 = \frac{16}{30} \times 100 = 53.33$$ Round up to next whole number: $$54$$ 5. **Step (c): Carmela's percent score** - Carmela scored 618 out of 800. Calculate: $$\text{Percent score} = \frac{618}{800} \times 100 = 77.25$$ Rounded to two decimals: $$77.25$$ **Final answers:** - Percentile rank for score 20: 4 - Percentile rank for score 68: 54 - Carmela's percent score: 77.25