Question

The annual rainfall in San Francisco is approximately normal with mean 22 inches and

standard deviation 7.9 inches. What is the probability that the rainfall in San Francisco

in the next year will be between 20 inches and 30 inches?

Answer 1

We have a normal distribution, $\mu=22, \sigma=7.9.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma};$

$z_1=\cfrac{20-22}{7.9}=-0.25;\\ z_2=\cfrac{30-22}{7.9}=1.01;\\ P(20<X<30)=P(-0.25<Z<1.01)=\\ =P(Z<1.01)-P(Z<-0.25)=$

$=0.8438-0.4013=0.4425$ ​(from z-table).