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Normal distrubution

  • Thread starter AllenHe
  • Start date
  • #1
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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.
 

Answers and Replies

  • #2
Matterwave
Science Advisor
Gold Member
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326
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.
 
  • #3
74
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oh.... thanks
 

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