Answer:
A) There is a 100% chance of meeting the height requirement for women.
B) There is a 99.89% chance of meeting the height requirement for men.
C) New height requirements are:
71.9 inches for men and 58.9 inches minimum for women.
At least 58.9 inches and at most 71.9 inches.
Step-by-step explanation:
This question involves finding z values which tell us the percentage from 0 to x.
z = (x-μ)/σ
A) In this question, the minimum sample point is 4 ft 9 inches or converting to inches, we have;(4*12) + 9 =57 inches.
The maximum sample point is 6 ft 4 inches which in inches gives; (6*12) + 4 = 76 inches
For the minimum point;
z = (57 - 63.3)/2.7 = -2.33
From the z-distribution table, this equates to 0.0099.
The maximum;
z = (76 - 63.3)/2.7 = 4.70
From the z-table, it gives 0.999.. Basically 100%.
So there is a 100% chance of meeting the height requirement for women.
B) For men;
the minimum z = (57 - 67.3)/2.8 = -3.68 which gives 0.00012 from the z-distribution table.
The maximum;
z = (76 - 67.3)/2.8 = 3.07 which gives 0.9989 from the z-distribution table. Basically, 99.89%.
So there is a 99.89% chance of meeting the height requirement for men.
C) To exclude the tallest 5% of men, we need to find the z-value for 0.95 and then solve for x.
Thus from the z-table, z = 1.65. So;
1.645 = (x - 67.3)/2.8
4.606 = x - 67.3
x = 67.3 + 4.606
x ≈ 71.9 inches for men.
So, Current minimum is okay.
To exclude the shortest 5% of women, we need to find the z for 0.05.
From the z-distribution table, it has a value of -1.645. So;
-1.645 = (x - 63.3)/2.7
-4.4415 = x - 63.3
x = 63.3 - 4.4415
x ≈ 58.9 inches minimum.
So, Current maximum is okay.
