td A survey found that women\'s heights are normally distributed with mean 63.8
ID: 2949886 • Letter: T
Question
td A survey found that women's heights are normally distributed with mean 63.8 in and standard deviation 2.2 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 women are eligible except the shortest 1% and the tallest 2%, what are the new height requirements? Click to view page 1 of the table. Click to view page 2 of the table. a. The percentage of women who meet the height requirement is 96. (Round to two decimal places as needed.) Are many women being denied the opportunity to join this branch of the military because they are too short or too tall? O A. Yes, because a large percentage of women are not allowed to join this branch of the military because of their height. Click to select your answer(s). 7Explanation / Answer
Solution:- Given that mean = 63.8, standard deviation = 2.2
a. P(58 < X < 80) = P((58-63.8)/2.2 < (x-mu)/sd < (80-63.8)/2.2))
= P(-2.6364 < Z < 7.3636)
= 0.9959
=> option B. No, because the percentage of women who meet the height requirement is fairly small.
b. => height of 1% tallest women = 63.8 - 2.326 * 2.2 = 58.6
=> height of 2% tallest women = 63.8 + 2.055 * 2.2 = 68.3
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.