A survey found that women\'s heights are normally distributed with mean 63.2 in

Question

A survey found that women's heights are normally distributed with mean 63.2 in and standard deviation 2.3 in. A branch of the military requires women's heights to be between 58 in and 80 in. Find the percentage of women meeting the height requirement. (Round to two decimal places.) b. Are many women being denied the opportunity to join this branch of the military because they are too short or too small? Yes, because a large percentage of women are not allowed to join this branch of the military because of their height. ii. No, because the percentage of women who meet the height requirement is fairly small. iii. No, because only a small percentage of women are not allowed to join this branch of the military because of their height. iv. Yes, because the percentage of women who meet the height requirement is fairly large.

Explanation / Answer

1) a) mean = 63.2 , s = 2.3

P( 58 < x < 80)

By normal distribution formula,

z = (x - mean) / s

= p( (58 - 63.2)/2.3 < z < ( 80 - 63.2) / 2.3)

= p(-2.26 < z < 7.30)

Now , we need to find p(-2.26 < z < 7.30)

p(58 < x < 80) = p(-2.26 < z < 7.30) = 0.9881 = 98.81%

b) answer is option 1)

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