Question

A survey found that​ women's heights are normally distributed with mean 63.5 in. and standard deviation 2.4 in. The survey also found that​ men's heights are normally distributed with mean 69.1 in. and standard deviation 3.6 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 55 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 ____​%. ​(Round to two decimal places as​ needed.) Since most men ____ (meet/do not meet) the height​ requirement, it likely that most of the characters are ▼ men/women. b. If the height requirements are changed to exclude only the tallest​ 50% of men and the shortest​ 5% of​ men, what are the new height​ requirements? The new height requirements are a minimum of ___. and a maximum of ___

Answer 1

a)

for normal distribution z score =(X-μ)/σx
here mean=       μ=	69.1
std deviation   =σ=	3.6000

percentage of men meeting the height requirement

probability =

P(55<X<62)

=

P(-3.917<Z<-1.972)=

0.0244-0=

0.0244~ 2.44%

Since most men do not meet the height​ requirement, it likely that most of the characters are women

b)

The new height requirements are a minimum of 63.2 and a maximum of 69.1