Question

A survey found that​ women's heights are normally distributed with mean 63.5 in. and standard deviation 2.9 in. The survey also found that​ men's heights are normally distributed with mean 67.6 in. and standard deviation 3.9 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?

The percentage of men who meet the height requirement is _________​%.

​(Round to two decimal places as​ needed.)

b. Since most men ______(“do not meet” or “meet”) the height​ requirement, it is likely that most of the characters are _______(“women” or “men”).

c. 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. ​(Round to one decimal place as​ needed.)

Answer 1

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