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

Given Data:

Mean(μ)=150

Standard Deviation(σ)=20

let the limits X, Y ==> X(lower limit) =130 and Y(upper limit)=170

It follows the normal distribution

the percentage of population between height 130 and 170

Now fist we find the Z score and we find the Z values from the Z-table

Normal distribution formula is given by

Z₁= (X-μ) / σ =(130-150) / 20 = -1

Z₂₌(X-μ) / σ =(170-150) /20 = 1

Now

Probability P(-1 < Z < 1) = P( Z < 1) - P( Z < -1) (because P(Z<1)-P(Z<-1)=p(-1 <Z<1) )

= 0.8413 - 0.1586 = 0.6827 ( from the below given Z value table)

Therefore the required percentage is 0.6827 × 100= 68.27

ANS=68.27 %

Z vlaues :

for positive Z values:

for negative Z- values: