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

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In summary, the door frames used in a department store are of one standard height, 1.83m. The heights of men in the store are normally distributed with mean 1.73m and standard deviation 0.064m. Women outnumber men in the store 19:1 and the proportion of women taller than the door frame is 0.00069. To find the proportion of people for whom a frame height of 1.83m would be too low, the probability of men and women taller than the door frames should be calculated separately, resulting in 19/20(0.00069)+1/20(0.0591). This means that the probability of the frame being too low for men is
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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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  • #2
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
oh... thanks
 

What does the proportion of people for a low door frame mean?

The proportion of people for a low door frame refers to the percentage of individuals who have reported encountering door frames that are too low for them to comfortably pass through.

How is the proportion of people for a low door frame calculated?

The proportion is calculated using the formula (19/20*0.99931+1/20*0.9409), which takes into account the total number of people surveyed and the percentage of those who reported issues with low door frames.

What does the result of this calculation represent?

The result of this calculation represents an estimate of the overall proportion of people who may encounter low door frames based on the data collected from a sample group.

What other factors could affect the proportion of people for a low door frame?

Other factors that could affect the proportion of people for a low door frame include the height and size of the surveyed population, the type of buildings and structures they frequent, and any physical limitations or conditions they may have.

Why is it important to consider the proportion of people for a low door frame?

Understanding the proportion of people for a low door frame can help architects, builders, and designers create more accessible spaces for individuals of all heights and abilities. It can also inform policies and regulations regarding building standards and accessibility.

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