Suppose that the length of research papers is uniformly distributed from 8 to 23 pages. We survey a class in which 55 research papers were turned in to a professor. We are interested in the average length of the research papers.Give the distribution of ΣX. (Round your standard deviation to three decimal places.)Calculate the probability that the professor will need to read a total of more than 930 pages.
Suppose that the length of research papers is uniformly distributed from 8 to 23 pages. We survey a class in which 55 research papers were turned in to a professor. We are interested in the average length of the research papers.Give the distribution of ΣX. (Round your standard deviation to three decimal places.)Calculate the
Given
That the length of the research paper is uniformly distributed from 8 to 23
so the distribution is uniform U(8,23)
a sample of 55 research papers are considered
n = 55
Find the distribution of
Also, calculate the probability that the professor will need to read a total of 930 pages
From the given information
Let X be a random variable indicates the length of the research papers that follows a uniform distribution
The given parameters are 8 and 23
X~U(8,23)
If the length of the paper is considered and we want to find the distribution of
The given sample size is 55 which can be considered a large sample
(If the sample size>30 we consider the sample as large )
From the Central limit theorem, the large sample always follows a normal distribution
CLT for sums:
If X1, X2...Xn follows any distribution then the sum of X with a large sample size follows the normal distribution
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