Final answer:
The student's question pertains to the uniform distribution of research paper lengths ranging from 10 to 25 pages. In this context, X represents the length of a research paper. Since the distribution is uniform, each page length from 10 to 25 is equally likely, and the expected value can be calculated as 17.5 pages.
Step-by-step explanation:
Understanding the Uniform Distribution of Research Paper Lengths
The student's question is concerned with the uniform distribution of research paper lengths in a particular class. When dealing with a uniform distribution, all outcomes in the specified range are equally likely. In the provided scenario, the length of research papers is uniformly distributed from 10 to 25 pages.
To answer part a, in words, X (the random variable) would represent the length of a research paper. For part b, we could describe the distribution of X as X~U(10,25), where U represents the uniform distribution and the numbers in the parentheses are the minimum and maximum lengths of the research papers, respectively.
As for the sample of 55 research papers, if we wanted to investigate the average length of these research papers, we would be looking at the sample mean of the distribution. Given the nature of the uniform distribution, we can also calculate the expected value of a research paper's length, which would be the average of the minimum and maximum values (10+25)/2 = 17.5 pages. However, when considering a sample, we look at the sample mean to approximate this expected value.