Question

For a continuous random variable that has a normal distribution with mean of 24 and a standard deviation of 6, find the area under the normal curve from 𝑥=18 and 𝑥=21.

Answer 1

We have a normal distribution, $\mu=24, \sigma=6.$

Let's convert it to the standard normal distribution, $z=\cfrac{x-\mu}{\sigma};$

$z_1=\cfrac{18-24}{6}=-1, \\z_2=\cfrac{21-24}{6}=-0.5,$

$P(18<X<21)=P(-1<Z<-0.5)=\\=P(Z<-0.5)-P(Z<-1)=$

$=0.30854-0.15866=0.14988$ ​(from z-table).