91Ó°ÊÓ

The length of the research papers is uniformly distributed from \(10\) to \(25\) pages. We survey a class in which \(55\) research papers were turned in to a professor. The \(55\) research papers are considered a random collection of all papers. We are interested in average length of research papers.

The random variable \(X\) is defined by

\(X=\) length of the research papers

Hence, the random variable \(X\) is length of the research papers.

The distribution of \(X\) is uniform.

The length of the research papers is uniformly distributed from \(10\) to \(2\) pages.

\(a = 10\)

\(b = 25\)

Therefore, \(X=U(a,b)=X=U(10,25)\)

\(X=U(10,25)\)

\(X=U(10,25)\)

Mean, \(\mu_{x}=\frac{a+b}{2}\)

\(=\frac{10+25}{2}\)

\(=\frac{35}{2}\)

\(=17.5\)

Hence, \(\mu_{x}=17.5\)