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 standard deviation of 30. if the library has 500 books, how many of the books have less than 180 pages.

As the mean is E[X] =150 and = 30, using the normal distribution to get the answer is just using Z. So, what we need is P(X<180). 



P(x<180) = P(z< 1) = (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:

I'm gonna have to say about 13 percent