Door Peephole Standing eye heights of women are normally distributed with a mean

Question

Door Peephole Standing eye heights of women are normally distributed with a mean of 1516 mm and a standard devation of 63 mm (based on anthropometric survey data from Gordon, Churchill, et al).  

A) a door peephole is placed at a height that is uncomfortable for women with standing eye heights greater than 1605 mm. what percentage of women will find that height uncomfortable?    

B) in selecting the height of a door peephole, the architect wants its height to be suitale for the highest 99% of standing eye heights of women. what standing eye height of women separates the highest 99% of standing eye heights from the lowest 1%?

Explanation / Answer

Z=(1605-1516)/63 =1.41

P( x>=1605) = P(z>=1.41) = 0.0793

7.93% are uncomfortable

in selecting the height of a door peephole, the architect wants its height to be suitale for the highest 99% of standing eye heights of women. what standing eye height of women separates the highest 99% of standing eye heights from the lowest 1%?

Z value for the lowest 1% = -2.326

X value = 1516 -2.326*63 =1369.46

Required height =1369.46mm

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