is Question: 10 pts Time Limit: 01.00.00 Submit Quitz 4 of 10 (0 complete)Y This

Question

is Question: 10 pts Time Limit: 01.00.00 Submit Quitz 4 of 10 (0 complete)Y This Quiz: 100 pts possible A survey found that women's heights are normally distributed with mean 63 8 in and standard deviation 22 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 opportunity to join this branch of the miltary 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 tal st 2%, atat aete whe t 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 (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 tail? O A. No. because the percentage of women who meet the height requirement is fairly smal. O B. Yes, because the percentage of women who meet the height réquirement is fairly large O C. No, because only a small percentage of women are not allowed to join this branch of the military becausé of their height O D. Yes, because a large percentage of women are not allowed topn this branch of the military because of their heght in and at most b. For the new height requirements, this branch of the military requires Round to one decimal place as needed.) women's heights to be at least Click to select your answers) e o

Explanation / Answer

Solution:- Given that information mean = 63.8, standard deviation = 2.2

a. P(58 < X < 80) = P((58-63.8)/2.2 < (x- mu)/sigma < (80 - 63.8)/2.2))
= P(-2.6364 < Z < 7.3636)
= P(Z < 7.3636) - P(Z < -2.6364)
= 1 - 0.0041
= 0.9959
= 99.59%
The percentage of women meet the height requment is 99.59%

The probability of women denied the opportunity is 1-0.9959 = 0.0041 = 0.41%

There fore,the percentage of women who denied the opportunity to join this branch of the military because they are too short or too tall is 0.41%

==> Option C. no because only a small percentage of women are nont allowed to join this branch of the military because of their height
  

b.
The height of the shortest 1% is,

Consider, P(X < x) = 0.01

P(X-mu)/sigma < (x-63.8)/2.2) = 0.01

(x-63.8)/2.2 = -2.326

x = 63.8 - (2.326*2.2) = 58.68

Therefore,the height of the shortest 1% is 58.68

The height of the tallest 2% is

Consider, P(Z > (x - 63.8)/2.2) = 0.02

x = 63.8 + (2.054*2.2)
x = 68.32

=> for the new height requirements, this branch of the military requires womens heights to be at least 57.7 in and at most 68.3 in.

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