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A survey found that​ women's heights are normally distributed with mean 63.1 in. and standard deviation...

A survey found that​ women's heights are normally distributed with mean 63.1 in. and standard deviation 2.3 in. The survey also found that​ men's heights are normally distributed with mean 69.6 in. and standard deviation 3.4 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 62 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?

b. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements? The new height requirements are a minimum of ? in. and a maximum of ? in.

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