Suppose that the length of research papers is uniformly distributed from 10 to 23 pages. We survey a class in which 55 research pa vere turned in to a professor. We are interested in the average length of the research papers. O Part (a) Part (b) Part (c) O Part (d) Ox= 4.33 |× (rounded to four decimal places) Part (e)

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**Analysis of Research Paper Length**

In this exercise, we analyze the distribution of research paper lengths. Suppose the length of research papers is uniformly distributed from 10 to 23 pages. A survey of a class, in which 55 research papers were submitted to a professor, was conducted to determine the average length of these papers.

### Parts of the Analysis

- **Parts (a) to (d):** Not visible.

- **Standard Deviation (σx):** Calculated to be 4.33 (rounded to four decimal places).

- **Parts (e) to (k):** Not visible.

### Probability Calculations

1. **Total Page Length Probability:**
   - Calculate the probability that the professor will need to read a total of more than 970 pages. (Answer should be rounded to four decimal places.)

2. **Individual Paper Length Probability:**
   - Find the probability that an individual paper is longer than 17 pages. (Answer should be rounded to four decimal places.)

3. **Average Paper Length Probability:**
   - Find the probability that the average length of 55 papers is more than 17 pages. (Answer should be rounded to four decimal places.)

### Percentile Calculations

- **Individual Papers' Length:**
  - Find the 65th percentile for the length of individual papers for a sample of 55 papers. (Answer should be rounded to two decimal places.)

- **Average Length of Papers:**
  - Find the 65th percentile for the average length of papers for the same sample size. (Answer should be rounded to two decimal places.)

### Additional Materials

- Further reading and resources are available to enhance understanding of the topic.

This content provides a framework for understanding how probability and statistics can be applied to real-world academic scenarios such as analyzing research paper lengths.
Transcribed Image Text:**Analysis of Research Paper Length** In this exercise, we analyze the distribution of research paper lengths. Suppose the length of research papers is uniformly distributed from 10 to 23 pages. A survey of a class, in which 55 research papers were submitted to a professor, was conducted to determine the average length of these papers. ### Parts of the Analysis - **Parts (a) to (d):** Not visible. - **Standard Deviation (σx):** Calculated to be 4.33 (rounded to four decimal places). - **Parts (e) to (k):** Not visible. ### Probability Calculations 1. **Total Page Length Probability:** - Calculate the probability that the professor will need to read a total of more than 970 pages. (Answer should be rounded to four decimal places.) 2. **Individual Paper Length Probability:** - Find the probability that an individual paper is longer than 17 pages. (Answer should be rounded to four decimal places.) 3. **Average Paper Length Probability:** - Find the probability that the average length of 55 papers is more than 17 pages. (Answer should be rounded to four decimal places.) ### Percentile Calculations - **Individual Papers' Length:** - Find the 65th percentile for the length of individual papers for a sample of 55 papers. (Answer should be rounded to two decimal places.) - **Average Length of Papers:** - Find the 65th percentile for the average length of papers for the same sample size. (Answer should be rounded to two decimal places.) ### Additional Materials - Further reading and resources are available to enhance understanding of the topic. This content provides a framework for understanding how probability and statistics can be applied to real-world academic scenarios such as analyzing research paper lengths.
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