Answer
given,
mean of women (μ)=63 inches
standard deviation of women (σ)= 2.4 inches
mean of men (μ)=70 inches
standard deviation of women (σ)= 2.5 inches
for women
[tex]P(x>66) [/tex]
[tex]P(x>66) = 1-P( \dfrac{x - \mu}{\sigma}<\dfrac{66-63}{2.4})[/tex]
[tex]P(x>66) = 1-P( z<\dfrac{3}{2.4})[/tex]
[tex]P(x>66) = 1-P( z<1.25)[/tex]
using z-table
[tex]P(x>66)= 1 - 0.8944[/tex]
[tex]P(x>66)=0.1056[/tex]
for men
[tex]P(x>66) [/tex]
[tex]P(x>66) = 1-P( \dfrac{x - \mu}{\sigma}<\dfrac{66-70}{2.5})[/tex]
[tex]P(x>66) = 1-P( z<\dfrac{-4}{2.5})[/tex]
[tex]P(x>66) = 1-P( z<-1.6)[/tex]
using z-table
[tex]P(x>66)= 1 - 0.0548[/tex]
[tex]P(x>66)=0.9452[/tex]
