Question

A survey found that women's heights are normally distributed with mean 62.7 in and standard deviation 3.9 in. The survey also found that men's heights are normally distributed with mean 69.9 in and standard deviation 3.4 in Most of the live characters employed at an amusement park have height requirements of a minimum of 57 in and a maximum of 64 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 % (Round to two decimal places as needed)

Answer 1

Solution:-
men : mean = 62.7, sd = 3.9

female : mean = 69.9, sd = 3.4

a. P(57 < X < 64) = P((57-69.9)/3.4 < (X-mean)/sd < (64-69.9)/3.4)
= P(-3.7941 < Z < -1.7353)
= 0.0408
= 4.08%

Thepercentge of men who meet the height requiremnt is 4.08%