Question

In: Statistics and Probability

A survey found that​ women's heights are normally distributed with mean 63.3 in. and standard deviation...

A survey found that​ women's heights are normally distributed with mean 63.3 in. and standard deviation 2.3 in. The survey also found that​ men's heights are normally distributed with mean 69.1 in. and standard deviation 3.1 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 57in. 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.)

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?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 69.1

standard deviation = = 3.1

a) P(57 < x < 62 ) = P[(57 - 69.1)/ 3.1) < (x - ) /  < (62 - 69.1) / 3.1) ]

= P(-3.90 < z < -2.29)

= P(z < -2.29) - P(z < -3.90)

Using z table,

= 0.0110 - 0

= 0.0110

The percentage of men who meet the height requirement is = 1.10%

b) Using standard normal table,

P(Z > z) = 50%

= 1 - P(Z < z) = 0.50  

= P(Z < z) = 1 - 0.50

= P(Z < z ) = 0.50

= P(Z < 0 ) = 0.50  

z = 0

Using z-score formula,

x = z * +

x = 0 * 3.1 + 69.1

x = 69.1

Using standard normal table,

P(Z < z) = 5%

= P(Z < z ) = 0.05

= P(Z < -1.645 ) = 0.05  

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 3.1 + 69.1

x = 64.0

The new height​ requirements is 69.1 in. and 64.0 in.


Related Solutions

A survey found that​ women's heights are normally distributed with mean 63.3 in. and standard deviation...
A survey found that​ women's heights are normally distributed with mean 63.3 in. and standard deviation of 3.7 in. The survey also found that​ men's heights are normally distributed with a mean 68.6 in. and standard deviation 3.3 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....
A survey found that​ women's heights are normally distributed with mean 62.4 in. and standard deviation...
A survey found that​ women's heights are normally distributed with mean 62.4 in. and standard deviation 3.1 in. The survey also found that​ men's heights are normally distributed with mean 69.3 in. and standard deviation 3.9 in. Consider an executive jet that seats six with a doorway height of 55.8 in. a. What percentage of adult men can fit through the door without​ bending? The percentage of men who can fit without bending is nothing​%. ​(Round to two decimal places...
A survey found that? women's heights are normally distributed with mean 63.9 in and standard deviation...
A survey found that? women's heights are normally distributed with mean 63.9 in and standard deviation 2.4 in. A branch of the military requires? women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too? tall? b. If this branch of the military changes the height requirements so that all...
A survey found that​ women's heights are normally distributed with mean 62.6 in. and standard deviation...
A survey found that​ women's heights are normally distributed with mean 62.6 in. and standard deviation 2.6 in. The survey also found that​ men's heights are normally distributed with a mean 67.6 in. and standard deviation 2.7. Complete parts a through c below. a. Most of the live characters at an amusement park have height requirements with a minimum of 4 ft 9 in. and a maximum of 6 ft 3 in. Find the percentage of women meeting the height...
A survey found that? women's heights are normally distributed with mean 62.7 in. and standard deviation...
A survey found that? women's heights are normally distributed with mean 62.7 in. and standard deviation of 3.4 in. The survey also found that? men's heights are normally distributed with mean of 69.3 in. and a standard deviation of 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 64 in. Complete parts? (a) and? (b) below. a)Find the percentage of men meeting the height...
A survey found that​ women's heights are normally distributed with mean 63.763.7 in and standard deviation...
A survey found that​ women's heights are normally distributed with mean 63.763.7 in and standard deviation 2.32.3 in. A branch of the military requires​ women's heights to be between 58 in and 80 in. a. Find the percentage of women meeting the height requirement. Are many women being denied the opportunity to join this branch of the military because they are too short or too​ tall? b. If this branch of the military changes the height requirements so that all...
A survey found that​ women's heights are normally distributed with mean 62.1 in. and standard deviation...
A survey found that​ women's heights are normally distributed with mean 62.1 in. and standard deviation 3.1 in. The survey also found that​ men's heights are normally distributed with mean 69.6 in. and standard deviation 3.7 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 in. and a maximum of 63in. Complete parts​ (a) and​ (b) below. a. Find the percentage of men meeting the height requirement. What does the...
A survey found that women's heights are normally distributed with mean 62.6 in. and standard deviation...
A survey found that women's heights are normally distributed with mean 62.6 in. and standard deviation 2.4 in. The survey also found that men's heights are normally distributed with mean 67.1 in. and standard deviation 3.4 in. Most of the live characters employed at an amusement park have height requirements of a minimum of 56 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...
A survey found that​ women's heights are normally distributed with mean 63.9 in. and standard deviation...
A survey found that​ women's heights are normally distributed with mean 63.9 in. and standard deviation 3.1 in. The survey also found that​ men's heights are normally distributed with mean 69.1 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 62 in. Complete parts​ (a) and​ (b) below. a. Find the percentage of men meeting the height requirement. What does...
A survey found that​ women's heights are normally distributed with mean 63.1 in. and standard deviation...
A survey found that​ women's heights are normally distributed with mean 63.1 in. and standard deviation 2.3 in. The survey also found that​ men's heights are normally distributed with mean 69.6 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 62 in. Complete parts​ (a) and​ (b) below. a. Find the percentage of men meeting the height requirement. What does...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT