Please Help!!!
The number of books borrowed weekly from a library follows a normal distribution with a mean of 190 and a standard deviation of 30. Which conclusion does this information best support?
There is a 16% chance that more than 250 books are borrowed in a week.

a)There is a 2.1% chance that more than 250 books are borrowed in a week.

b)There is a 68% chance that fewer than 250 books are borrowed in a week.

c)There is an 84% chance that more than 250 books are borrowed in a week.

d)There is an 84% chance that fewer than 250 books are borrowed in a week.

Question

Please Help!!!
 The number of books borrowed weekly from a library follows a normal distribution with a mean of 190 and a standard deviation of 30. Which conclusion does this information best support?
There is a 16% chance that more than 250 books are borrowed in a week. 

a)There is a 2.1% chance that more than 250 books are borrowed in a week.

b)There is a 68% chance that fewer than 250 books are borrowed in a week.

c)There is an 84% chance that more than 250 books are borrowed in a week.

d)There is an 84% chance that fewer than 250 books are borrowed in a week.

anonymous · Answer

Find the probabilities of more than 250 books are borrowed and of less than 250 books getting borrowed. Let $X$ be the number of borrowed books, then $$\begin{align*}P(X>250)&=P\left(\frac{X-190}{30}>\frac{250-190}{30}\right)\ &=P\left(Z>2\right)\ &\text{and}\ P(X<250)&=P(Z<2) \end{align*}$$