Question

Suppose that people's heights (in centimeters) are normally distributed with a mean of 170 and a standard deviation of 5. We find the heights of 50 people.

Answer 1

We have
mean=mu=170
standard deviation=sigma=5

can now calculate the Zmin and Zmax using Z=(X-mean)/standard deviation
Zmin=(165-170)/5=-1
Zmax=(175-170)/5=+1
From normal probability tables,
P(z<Zmin)=P(z<-1)=0.15866
P(z<Zmax)=P(z<+1)=0.84134
P(165<x<175)=P(Zmin<z<Zmax)=0.84134-0.15866= 0.68269