SOLUTION: Books in the library are found to have average length of 350 pages with standard deviation of 100 pages. What is the probability that a randomly selected book will be 150 pages or
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Question 984932: Books in the library are found to have average length of 350 pages with standard deviation of 100 pages. What is the probability that a randomly selected book will be 150 pages or less? (Hint: Sketch the distribution curve Answer by mathmate(429) (Show Source):
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Given:
Library books are found to have a mean of 350 pages and a standard deviation of 100 pages.
Need:
The probability that a book is found to have 150 pages or less.
Solution:
The question did not mention the distribution of the pages. We will assume that the number of pages of the books has normal distribution (or Gaussian).
The population (the whole library) mean is 350 pages, and population standard deviation is 100 pages.
Therefore books 150 pages or less are 350-2*100 pages or less, or in statistics notation, , and we need the probability , where
This probability is obtained from the Normal Distribution table (left tail) for Z=-2 as 0.0225.
Note: the small area where Z<0 has been subtracted to get probability = 0.0225.
Answer:
Therefore the required probability of finding books 150 pages or less is approximately 0.0225.
