Question

The distribution of height of adult male of a particular race is normally distributed with

mean 165 cm and variance 36 cm. find the probability of an adult male to have height

between 150 cm and 180 cm. [given that 0 ≤ Z ≤ 2.5 = 0.4938]

Answer 1

$P(z<180)=\frac{180-165}{\sqrt{36}}=2.5$

$P(z<150)=\frac{150-165}{\sqrt{36}}=-2.5$

$P(150<x<180)=P(-2.5<z<2.5)=2P(0 ≤ Z ≤ 2.5 )=2\cdot0.4938=0.9876$