Answer: 68.27%
Explanation:
We assume that the world human population heights follow a perfect normal distribution.
Given : Population mean : [tex]\mu=150[/tex]
Standard deviation : [tex]\sigma=20[/tex]
Let X be the random variable that represents the height of population.
Z-score : [tex]z=\dfrac{x-\mu}{\sigma}[/tex]
For x=130
[tex]z=\dfrac{130-150}{20}=-1[/tex]
For x=170
[tex]z=\dfrac{170-150}{20}=1[/tex]
By using the standard normal distribution table for z , we have
P-value =[tex]P(130<x<150)=P(-1<z<1)=P(z<1)-P(z<-1)[/tex]
[tex]=0.8413447-0.1586553\\=0.6826894\approx0.6827\approx68.27\%[/tex]
Hence, the percentage of the population would have a height between 130 and 170 = 68.27%
