Question

Suppose that the length of research papers is uniformly distributed from ten 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 the average length of the research papers.

a. In words, \(X= \)

b. \(X= ( , )\)

c. \(\mu_{x}= \)

Short answer

Part a. \(X=\) length of the research papers.

Part b. \(X=U(10,25)\)

Part c. \(\mu_{x}=17.5\)

Step-by-step solution

Part a. Step 1. Given information

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.

Part a. Step 2. Calculation

The random variable \(X\) is defined by

\(X=\) length of the research papers

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

Part b. Step 1. Calculation

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

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

Part c. Step 1. Calculation

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

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

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

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

\(=17.5\)

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