A survey found that women's heights are normally distributed with mean

63.2

in. and standard deviation

2.6

in. The survey also found that men's heights are normally distributed with mean

69.6

in. and standard deviation

3.9

in. Most of the live characters employed at an amusement park have height requirements of a minimum of

57

in. and a maximum of

63

in. Complete parts (a) and (b) below.

Question content area bottom

Part 1

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

enter your response here%.

(Round to two decimal places as needed.)

Part 2

Since most men

do not meet

meet

the height requirement, it is likely that most of the characters are

women.

men.

Part 3

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

enter your response here

in. and a maximum of

enter your response here

in.

(Round to one decimal place as needed.)