The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distrib

Cheyanne Leigh 2021-02-11 Answered
The stature of men is normally distributed, with a mean of 69.0 inches and a standard deviation of 2.8 inches. The height of women is normally distributed, with a mean of 63.6 inches and a standard deviation of 2.5 inches. Modeling academy standards require women to be models taller than 66 inches (or 5 feet 6 inches). What percentage of women meet this requirement?
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casincal
Answered 2021-02-12 Author has 82 answers

Step 1 From the given information, the mean of women is 63.6 inches and standard deviation is 2.5 inches. Let X be the height of the women follows normal distribution with μ=63.6 and σ=2.5. Modeling academy standards require women to be models taller than 66 inches Step 2 The percentage of women meet this requirement is, Percentage =P(X > 66)×100%
=P(X  μσ > (66  μ)σ)×100%
=P(z > 66  63.62.5)×100%
=P(z > 0.96)×100%
=[1  P(z  0.96)]×100%
=0.1685×100% from the excel function, =1  NORM.DIST(0.96, 0, 1, TRUE)
=16.85%

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