A survey found that women\'s heights are normally distributed with mean 63 4 in

Question

A survey found that women's heights are normally distributed with mean 63 4 in and standard deviation 2.4 in. A branch of the mlitary 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 opportunilty to join this branch of the military because they are too short or too tal b.If this branch ofthe miitary changes te height requirements so tat al women are eligble except he shortest 1% and te talest 2%, whut uo tonew height requr morts? Click to view page 1 of the table, Cick to view page 2 of the table a. The percentage of women who meet the height requirement is Round to two decimal places as needed.) Are many women being denied the opportunity to join this branch of the miltary because they are too short or too tall? A. Yes, because he percentage of women who meet the height requirement is fainy large. O B. No, because the percentage of women who meet the height requirement is fairly smal OC. because only a smal percentage of women ar" not allowed tDjoin this branch of the matary becauseoftheir height O D. Yes, because a large 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 leastin and at mostn Round to one decimal place as needed.) Click to select your answerls).

Explanation / Answer

A. mean = 63.4

s.d. = 2.4

Z58 = (X - ) /
Z58= (58 - 63.4) / 2.4

Z58= -2.25

Z88 = (X - ) /
Z88 = (80 - 63.4) / 2.4

Z88 = 6.91667

Probability between -2.25 and 6.91667 is 0.9878

i.e. 98.78% women meets the height requirements.

Only (100-98.78)% = 1.22% of women were denied.

Not many women are denied. ( Option C)

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