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.)
Question
Answer:
98.93
Step-by-step 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%