Proportion of People for Door Frame Too Low: 19/20*0.99931+1/20*0.9409

[AllenHe]

Homework Statement

The door frames used by a builder are of one standard height, 1.83m. The heights of men are normally distributed with mean 1.73m and standard deviation 0.064m.
The door frames are to be used in a department store. It is known that women outnumber men in the ratio 19:1 in the store and the proportion of women taller than the door frame is 0.00069.
Find the proportion of people for whom a frame height of 1.83m would be too low.

Homework Equations

The Attempt at a Solution

I thought it should be 19/20*(0.99931)+1/20*(0.9409)
But the answer is 19/20(0.00069)+1/20(0.0591)
But 0.00069 and 0.0591 are the probabilities for men and women taller than the door frames.
So i don't understand.

 

[Matterwave]

The question is to find the proportion of people for whom the frame is "too low". This means that the door is too short for these people.

 

[AllenHe]

oh... thanks