Question

A survey found that women's heights are normally distributed with mean 63.7 in. and standard deviation 3.6 in. The survey also found that men's heights are normally distributed with mean 68.4 in. and standard deviation 3.8 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in. and a maximum of 62 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?

 The percentage of men who meet the height requirement is _______ %

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean= 68.4

S.d = 3.8

We need to find

P(57

P(x<62)

Z = (62 - 68.4)/3.8

Z = -1.68

From z table, P(z<-1.68) = 0.0465

P(x<57)

Z = (57-68.4)/3.8 = -3

From z table, P(z<-3) = 0.0013

Required answer is 0.0465 - 0.0013

= 0.0452

Or 4.52%