Question

The numbers 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 book have less than than 180 pages

Answer 1

420 books

Explanation:

The number of pages in the books follow a Normal distribution, so we can use z-value to find the probability(percentage) of books that will have less than 180 pages and using that we can calculate how many books out of 500 will have less than 180 pages.

Mean number of pages = 150

Standard deviation = 30

Converting 180 to z-value:

`z=(180-150)/(30)=1`

Thus we need to find what percentage of values in a normal distribution are below z score of 1 . This can be done by using z-tables. Using the z-table, we find that the probability that the value will be less than 1 is 0.8413 or 84.13%

Thus 84.13% of books will have less than 180 pages. So, out of 500 the books that will have less than 180 pages will be:

0.8413 x 500 = 420

Therefor, 420 books will have less than 180 pages.