Question

A survey found that​ women's heights are normally distributed with mean 63.6 in. and standard deviation 2.4 in. The survey also found that​ men's heights are normally distributed with mean 67.1 in. and standard deviation 3.8 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in. and a maximum of 64 in. Complete parts​ (a) and​ (b) below. a. Find the percentage of men meeting the height requirement. What does the result suggest about the genders of the people who are employed as characters at the amusement​ park?

Answer 1

a)
Here, μ = 67.1, σ = 3.8, x1 = 55 and x2 = 64. We need to compute P(55<= X <= 64). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (55 - 67.1)/3.8 = -3.18
z2 = (64 - 67.1)/3.8 = -0.82

Therefore, we get
P(55 <= X <= 64) = P((64 - 67.1)/3.8) <= z <= (64 - 67.1)/3.8)
= P(-3.18 <= z <= -0.82) = P(z <= -0.82) - P(z <= -3.18)
= 0.2061 - 0.0007
= 0.2054
= 20.54%

b)
This indicates that only 20.54% are employable however the remaining requirements will be fulfilled by women.
Most of the people who are employed as characters at the amusement​ park are women