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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.

Respuesta :

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

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

P(x<180) = P(z< 1) = [tex]\phi [/tex](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:
[tex]0.8413 * 500 = 420.65[/tex]

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