<img src="//img.wizedu.com/questions/e138b710-cddd-11ec-b542-9b7bb9a66004.jpg" title="1626232088410838.jpg" alt="7CB069AE-E873-4DD7-B52B-F0BF616C37C6.jpeg"/>A survey found that women's heights are normally distributed with mean \(63.6\) in. and standard deviation \(3.4\) in. The survey also found that men's heights are normally distributed with mean \(69.7\) 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.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 \(\square \%\). (Round to two decimal places as needed.)

Given:For women :Mean = <img src="//img.wizedu.com/questions/e1c26680-cddd-11ec-8b2f-63c2c6e8c61d.png"/> = 62.4Standard deviation = <img src="//img.wizedu.com/questions/e2434910-cddd-11ec-b987-c5a27fe7ee25.png"/> = 3.7Let X be the women's heights are normally distributed.For women :Mean = <img src="//img.wizedu.com/questions/e1c26680-cddd-11ec-8b2f-63c2c6e8c61d.png"/> = 69.1Standard deviation = <img src="//img.wizedu.com/questions/e2434910-cddd-11ec-b987-c5a27fe7ee25.png"/> = 3.6Let X be the men's heights are normally distributed<img src="//img.wizedu.com/questions/e2fdc060-cddd-11ec-972e-1530ef8ae3e7.png" title="1626338962126618.png" />Thereforea) The percentage of men who meet the height requirement is 7.70 %

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Find the percentage of men meeting the height requirement

A survey found that women's heights are normally distributed with mean \(63.6\) in. and standard deviation \(3.4\) in. The survey also found that men's heights are normally distributed with mean \(69.7\) 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.

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 \(\square \%\). (Round to two decimal places as needed.)

Solutions

Expert Solution

Given:

For women :

Mean = = 62.4

Standard deviation = = 3.7

Let X be the women's heights are normally distributed.

For women :

Mean = = 69.1

Standard deviation = = 3.6

Let X be the men's heights are normally distributed

Therefore

a) The percentage of men who meet the height requirement is 7.70 %

Amanda K answered 2 years ago

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