Question

Assume the world human population heights follow a perfect normal distribution with standard deviation of 20 and mean of 150, what percentage of the population would have a height between 130 and 170?

Answer 1

Answer: 68.27%

Step-by-step explanation:

We assume that the world human population heights follow a perfect normal distribution.

Given : Population mean :
`\mu=150`

Standard deviation :
`\sigma=20`

Let X be the random variable that represents the height of population.

Z-score :
`z=(x-\mu)/(\sigma)`

For x=130

`z=(130-150)/(20)=-1`

For x=170

`z=(170-150)/(20)=1`

By using the standard normal distribution table for z , we have

P-value =
`P(130<x<150)=P(-1<z<1)=P(z<1)-P(z<-1)`

`=0.8413447-0.1586553\\=0.6826894\approx0.6827\approx68.27\%`

Hence, the percentage of the population would have a height between 130 and 170 = 68.27%