Suppose that the length of research papers is uniformly distributed from 10 to 25 pages. We survey a class in which 55 research papers were turned into a professor. The 55 research papers are considered a random collection of all papers. Let X denote the average length of the research papers. (a) Calculate the probability that the average length of the papers is at most 17 pages long. Shade the appropriate area on the distribution. Scale and label your axes. w (b) What is the 90th percentile for the average length of the papers? Shade the appropriate area on the distribution. Scale and label your axes. Use proper units. (c) How would your answers for parts (a) and (b) change if the sample size had been 20?

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