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

$\mu = 165 \\ \sigma^2 = 36 \\ \sigma= 6 \\ P(150<X<180) = P(X<180) -P(X<150) \\ = P(Z< \frac{180-165}{6}) -P(Z< \frac{150-165}{6}) \\ = P(Z<2.5) -P(Z< -2.5) \\ = 0.9937 -0.0062 \\ = 0.9875$