A survey found that​ women's heights are normally distributed with mean 62.1 in. and standard deviation 3.3 in. The survey also found that​ men's heights are normally distributed with mean 67.9 in. and standard deviation 3.4 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 in. and a maximum of 62in. Complete parts​ (a) and​ (b) below.   a. Find the percentage of men meeting the height requirement.

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A survey found that​ women's heights are normally distributed with mean 62.1 in. and standard deviation 3.3 in. The survey also found that​ men's heights are normally distributed with mean 67.9 in. and standard deviation 3.4 in. Most of the live characters employed at an amusement park have height requirements of a minimum of
55 in. and a maximum of 62in. 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?
 
The percentage of men who meet the height requirement is
nothing​            %.
 
 
Expert Solution
Step 1

Let X be the random variable that denotes the women's heights.

Let Y be the random variable that denotes the men's heights.

Mathematically,

X~Nμx=62.1,σx2=3.32

Y~Nμy=67.9,σy2=3.42

Z=X-μxσx~N0,1

Z=Y-μyσy~N0,1

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