Question

The height of the students at a particular university is normally distributed with a mean of 63 inches and a standard deviation of 3 inches. There are 5000 students at this university. How many students have a height between 60 to 66 inches?

Answer 1

$z=\frac{x-\mu}{\sigma/\sqrt n}$

$z_1=\frac{60-63}{3}=-1.00$

$z_2=\frac{66-63}{3}=1.00$

$P(60<x<66)=P(z<1)-P(z<-1)=0.8413-0.1587=0.6826$

number of students who have a height between 60 to 66 inches:

$5000\cdot 0.6826=3413$