Question

A survey found that​ women's heights are normally distributed with mean 62.2 in. and standard deviation 3.9 in. The survey also found that​ men's heights are normally distributed with mean 69.3 in. and standard deviation 3.1 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. please show steps

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 do not meet the height​ requirement, it is likely that most of the characters are 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 in. and a maximum of in.

​(Round to one decimal place as​ needed.)

Answer 1

Please don't hesitate to give a "thumbs up" in case you're satisfied with the answer

Women :
Mean = 62.2 inch
Stdev = 3.9 inch

Men: 69.3 inch
Stdev: 3.1 inch

Min and Max : 57 to 64

a. %age of men meeting the height requirement:
P(57<X<64)
= P( (57-69.3)/3.1 <Z< (64-69.3)/3.1))
= P(-3.97<Z<-1.71)
= .04366 to 4.40%

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

b. Tallest 50% of men and shortest men can be found like this:

Tallest 50% of men is basically such that :
P(X<c1) = .50
c1 = 69.3 inch

Shortest 5%:
P(X<c2) = .05
(c2 - 69.3)/3.1 = -1.645
c2 = 3.1*-1.645 + 69.3 = 64.2

New height requirements are : 64.2 to 69.3