Question

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.

Answer 1

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= (x-E[X])/(\sigma ) = (180-150)/(30) = (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`