Question

The weights of the Grade 11 students are known to be normally distributed with a mean of 54 kg and a standard deviation of 8 kg. Find the percentage of Grade 11 students with weights between 45 kg and 66 kg.

Answer 1

We have a normal distribution, $\mu=54, \sigma=8.$

Let's convert it to the standard normal distribution,

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

$z_1=\cfrac{45-54}{8}=-1.13;\\ z_2=\cfrac{66-54}{8}=1.50;\\ P(45<X<66)=P(-1.13<Z<1.50)=\\ =P(Z<1.50)-P(Z<-1.13)=\\ =0.9332-0.1292=0.8040 \text{ (from z-table).}$