Question

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

62.6

in. and standard deviation

3.3

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

68.9

in. and standard deviation

3.8

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

nothing​%.

​(Round to two decimal places as​ needed.)

Since most men

▼

do not meet

meet

the height​ requirement, it is 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

nothing

in. and a maximum of

nothing

in.

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

Answer 1

(A)

Let X is a random variable shows the men's height. Here X has normal distribution with parameters

The z-score for X = 55 inches is

The z-score for X = 62 inches is

The percentage of men who meet the height requirement is

Answer: 3.43%

The percentage of men who meet the height requirement is 3.43​%.

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

b)

The z-score 1.645 has 0.05 area to its right.

The upper limit of new height is

The z-score -1.645 has 0.05 area to its left.

The lower limit of new height is

The new height requirements are at least 62.6 in and at most 75.2 in.