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zloy xaker [14]
3 years ago
15

The number of pages in the books in a library follow a normal distribution. The mean number of pages in a book is 150 with a sta

ndard deviation of 30. if the library has 500 books, how many of the books have less than 180 pages.
Mathematics
1 answer:
AysviL [449]3 years ago
7 0
As the mean is E[X] =150 and \sigma = 30, using the normal distribution to get the answer is just using Z. So, what we need is P(X<180). 

Z=  \frac{x-E[X]}{\sigma } = \frac{180-150}{30} =  \frac{30}{30} = 1

P(x<180) = P(z< 1) = \phi(1) = 0.8413. 

Then, just multiplying the amount of books you have, which is 500, with the probability would give how many books are less than 180 pages, being:
0.8413 * 500 = 420.65
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