document.write( "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 \n" ); document.write( "

Algebra.Com's Answer #605837 by mathmate(429) $\"\"$ $\"About$

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\n" ); document.write( "Given:
\n" ); document.write( "Library books are found to have a mean of 350 pages and a standard deviation of 100 pages.
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\n" ); document.write( "Need:
\n" ); document.write( "The probability that a book is found to have 150 pages or less.\r
\n" ); document.write( "\n" ); document.write( "Solution:
\n" ); document.write( "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).
\n" ); document.write( "The population (the whole library) mean is 350 pages, and population standard deviation is 100 pages.
\n" ); document.write( "Therefore books 150 pages or less are 350-2*100 pages or less, or in statistics notation, $\"mu-2%2Asigma+=+150\"$ , and we need the probability
\n" ); document.write( " $\"P%28X+%3C+mu+-+2%2Asigma%29=P%28Z+%3C+2%29\"$ , where $\"Z=%28X-mu%29%2Fsigma\"$
\n" ); document.write( "This probability is obtained from the Normal Distribution table (left tail) for Z=-2 as 0.0225.
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\n" ); document.write( "Note: the small area where Z<0 has been subtracted to get probability = 0.0225.
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\n" ); document.write( "Answer:
\n" ); document.write( "Therefore the required probability of finding books 150 pages or less is approximately 0.0225. \n" ); document.write( "

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