Question

The door frames used by abuilder of one standard height 1.830 m the hights of men are normally distributed with mean 1.730 m ansfadard deviation 0.064 m. a) find the proportion of men that will be taller the door frame .b) find the frame height such that one man in a thousand will be taller then the frame height.

Answer 1

a) $P(X>1.830)=P(Z>\frac{1.830-1.730}{0.064}=P(Z>1.56)=0.0594.$

b) $P(Z>z)=0.001$

$P(Z<z)=0.999$

$z=3.09$

$\frac{x-1.730}{0.064}=3.09$

$x=3.09*0.064+1.730=1.928\; m.$