A survey found that women\'s heights are normally distributed with mean 63.9 in

Question

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 women are eligible except the shortest 1% and the tallest 2% requirements? Click to view page 1 of the table. Click to view page 2 of the table at are the new e t 1% a. The percentage of women who rmeet the height requirement is (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. No, because the percentage of women who meet the height requirement is fairly small O B. Yes, because a large percentage of women are not allowed to join this branch of the military because of their height. O C. No, because only a small percentage of women are not allowed to join this branch of the military because of their height. O D. Yes, because the percentage of women who meet the height requirement is fairly large in b. For the new height requirem ents, this branch of the military requires women's heights to be at least Round to one decimal place as needed.) in and at most

Explanation / Answer

Solution:- mean = 63.9in,sd = 2.4in formula z = (x - µ)/

a. P(58 < x < 80) = P((58 - 63.9)/2.4 < Z <  (80 - 63.9)/2.4)

= P(-2.46 < Z < 6.71)

=  0.9931

==> the precentage of women who meeting the height reqirement is 99.31%

---> option C. No, because only a small percentage of women are not allowed to join this branch of the military because of their height.

b. For the new height requirements, this branch of the military requires women's heights to be at least 58.3 in and at most 68.8 in.

*shortest 1% = 0.0100 0.0099 (value of -2.33)

*tallest 2% = 0.9800 0.9798 (value of 2.05)

*µ + (x × )

63.9 + (-2.33 × 2.4) = 58.30

63.9 + (2.05 × 2.4) = 68.82

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