A survey found that women's heights are normally distributed with mean 63.4 in. and standard deviation 2.9 in. The survey also found that men's heights are normally distributed with mean 68.8 in. and standard deviation 3.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 63 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
3.10%.
(Round to two decimal places as needed.)
Since most men
do not meet
meet
do not meet
the height requirement, it is likely that most of the characters are
women.
men.
women.
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
62.8 in. and a maximum of
68.9 in.
(Round to one decimal place as needed.)