Final answer:
The possible range of scores for the nth student in a class with an average of 88 can theoretically be from 0 to 100; however, practical educational scoring boundaries may restrict this range to between the lowest passing grade and 100.
Step-by-step explanation:
The question involves determining the possible range of integers for the nth student's score given that the average score for the class is 88 and all scores are integers. To find the possible score range for the nth student, we must consider the highest and lowest scores that could be achieved by a student given the integer nature of the scores and the fixed average.
If we assume the nth student has the lowest possible score, the rest of the 54 students would need to score as high as possible to maintain the average of 88. Thus, if the nth student scored 0 (as the lowest possible integer for a test score), the total sum of the scores from the remaining 54 students would need to be 54 times 88 plus 88 (the average including the nth student's score). This is not realistic as the other students' scores would also be integers and would need to exceed 100 (a typical maximum score) to balance the nth student's 0. Conversely, if the nth student scored the maximum of 100 (assuming 100 is the typical maximum test score), the remaining 54 students would need to have their scores lowered to balance out to the average of 88.
Considering the likely score bounds set by most educational institutions, the lowest score could be 0 and the highest could generally be 100. However, practical educational constraints such as passing scores and maximum scores should be considered, making the typical range somewhere between the typical passing grade (such as 50 or 60) and the maximum achievable score (often 100).