Question

A survey found that women's heights are normally distributed with mean 62.3 in. and standard deviation 2.3 in. The survey also found that men's heights are normally distributed with a mean 67.6 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 9 in. and a maximum of 6 ft 4 in. Find the percentage of women meeting the height requirement The percentage of women who meet the height requirement is %. (Round to two decimal places as needed.)​

Answer 1

98.93

Explanation:

we're looking for

4 ft 9 <x<6 ft 4

Let's convert this into inches

4 ft 9 = 57 in

6 ft 4= 76

so we're looking for

57<x<76

which is equal to

p(76)-p(57)

let's start by p(76)

(76-62.3)/2.3= 5.946521 which on a ztable is equal to 1

p(57)=

(57-62.3)/2.3= -2.3

which is equal to 1-.9893= .0107

Finally,

1-.0107= .9893 = 98.93%