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Door Peephole
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Door Peephole. Standing eye heights of women are normally distributed with a mean of 1516 mm and a standard deviation 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 suitable 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%?
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Answer:
a)
X ~ N ( µ = 1516 , σ = 63 )
P ( X > 1605 ) = 1 - P ( X < 1605 )
Standardizing the value
Z = ( X - µ ) / σ
Z = ( 1605 - 1516 ) / 63
Z = 1.41
P ( ( X - µ ) / σ ) > ( 1605 - 1516 ) / 63 )
P ( Z > 1.41 )
P ( X > 1605 ) = 1 - P ( Z < 1.41 )
P ( X > 1605 ) = 1 - 0.9207 (from Z table)
P ( X > 1605 ) = 0.0793
= 7.93%
b)
P ( X > x ) = 1 - P ( X < x ) = 1 - 0.99 = 0.01
To find the value of x
Looking for the probability 0.01 in standard normal table to calculate Z score = -2.3263
Z = ( X - µ ) / σ
-2.3263 = ( X - 1516 ) / 63
X = 1369.44
