For the binomial distribution, the number of trials \(n\) is a fixed number. Let \(Y\) denote that \(50 \%\) score has been obtained by a randomly selected university student who studies four subjects. Let \(X\) denote number of subjects in which \(50 \%\) score had been obtained by a randomly selected university student (i.e., the number of subjects could be any number). A binomial distribution approximates well the probability distribution for one of \(Y\) and \(X\), but not for the other.

a. Explain why.

b. Identify the case for which the binomial applies, and identify \(n\) and \(p\).