Question

The mean height of the grade nine students at a certain high school is 164 centimeters and the

standard deviation is 10 centimeters. Assuming the heights are normally distributed, what

percent of the heights is greater than 168 centimeters?

Answer 1

We have a normal distribution, $\mu=164, \sigma=10.$

Let's convert it to the standard normal distribution,

$z=\cfrac{x-\mu}{\sigma}=\cfrac{168-164}{10}=0.40;$

$P(X>168)=P(Z>0.40)=\\ =1-P(Z<0.40)=\\ =1-0.6554=0.3446=34.46\%\text{ (from z-table)}.$