Question

please explain the result

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

62.7

in. and standard deviation

2.2

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

68.9

in. and standard deviation

2.9

Complete parts a through c below.

a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft

99

in. and a maximum of 6 ft

2

in. Find the percentage of women meeting the height requirement.The percentage of women who meet the height requirement is

b. Find the percentage of men meeting the height requirement.

The percentage of men who meet the height requirement is

c. If the height requirements are changed to exclude only the tallest​ 5% of men and the shortest​ 5% of​ women, what are the new height​ requirements?

The new height requirements are at least

and at most

in.

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

Answer 1

Given that A survey found that​ women's heights are normally distributed with mean 62.7 in. and standard deviation 2.2 in.

Given that A survey found that​ women's heights are normally distributed with mean 68.9 in. and standard deviation 2.9 in.

Requirement is to have minimum height of of 4 ft 9 in (57 in.) and maximum height  of 6 ft 2 in (74 in.)

a) The probability,

The percentage of women who meet the height requirement is

b) The probability,

The percentage of men who meet the height requirement is

c) Tallest 5% of men is such that,

Shortest​ 5% of​ women is such that,

The new height requirements are at least in. and at most in.