Question

The ages of a certain group of students in a junior high school follow a normal

distribution with a mean of 13 and a standard deviation of 1.5. Find the probability

that a randomly selected student is between 10-16 years old.

Answer 1

We have a normal distribution, $\mu=13, \sigma=1.5.$

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

$z_1=\cfrac{10-13}{1.5}=-2, \\z_2=\cfrac{16-13}{1.5}=2,$

$P(10<X<16)=P(-2<Z<2)=\\=P(Z<1.5)-P(Z<-1.5)=$

$=0.9332-0.0668=0.8664$ ​(from z-table).