Question

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

63.763.7

in. and standard deviation

3.43.4

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

69.169.1

in. and standard deviation

3.63.6

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

5656

in. and a maximum of

6464

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?

Answer 1

= 69.1

= 3.6

To find P(56 < X < 64):

For X = 56:

Z = (56 - 69.1)/3.6

= - 3.6389

By Technology, Cumulative Area Under Standard Normal Curve = 0.0001

For X = 64:

Z = (64 - 69.1)/3.6

= - 1.4167

By Technology, Cumulative Area Under Standard Normal Curve = 0.0783

So

P(56 < X < 64):=0.0783 - 0.0001 = 0.0782 =7.82%

So,

Answer is:

7.82%

Since the percentage of men meeting the height requirement is only 7.82%, the result suggests that most of the people who are employed as characters at the amusement​ park are women.