In his NPR radio program "A Prairie Home Companion," Garrison Keillor describes the mythical town of Lake Wobegon as a place where "all the women are strong, all the men are good-looking, and all the children are above average." The average (mean) score on a recent test given to a class of 30 students at Lake Wobegon Elementary School was 75 (out of 100).

Question

In his NPR radio program "A Prairie Home Companion," Garrison Keillor describes the mythical town of Lake Wobegon as a place where "all the women are strong, all the men are good-looking, and all the children are above average." The average (mean) score on a recent test given to a class of 30 students at Lake Wobegon Elementary School was 75 (out of 100). 
(a) explain why it is possible for every student in the class to have scored above average on the test. 
(b) what is the largest number of students who could have scored above average on the test?

The thing that comes to mind immediately is how the average is rounded. What if all students made a score of 75.01? The average, rounded, is 75, but all students were above average.