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

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SUMMARY

The discussion centers on calculating the proportion of individuals for whom a standard door frame height of 1.83m is insufficient. The heights of men are normally distributed with a mean of 1.73m and a standard deviation of 0.064m. Given the ratio of women to men in the store is 19:1, the correct formula to determine the proportion of people for whom the door frame is too low is 19/20*(0.00069) + 1/20*(0.0591), where 0.00069 and 0.0591 represent the probabilities of women and men exceeding the door height, respectively. This calculation clarifies the misunderstanding regarding the appropriate probabilities to use in the context of the problem.

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AllenHe
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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.
 
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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.
 
oh... thanks
 

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