Posted by jimmy on .
Assume that women's heights are normally distributed with a mean=63.6 in. and standard deviation = 2.5 in.
a) To be eligible for the US Marine Corps, a woman must have a height between 58 in. and 73 in. Find the percentage of women who satisfy that requirement.
b)If the requirement is changed to exclude the shortest 1% and exclude the tallest 1%, find the heights that are acceptable.
Use z-scores for both a) and b).
z = (x - mean)/sd
a) Find both z-scores.
First z: x = 58, mean = 63.6, sd = 2.5
Second z: x = 73, mean = 63.6, sd = 2.5
Once you have both z-scores, check a z-table for the probability between the two scores. Convert to a percentage.
b) Find the two z-scores using a z-table for the shortest 1% and the tallest 1%. Once you have both z-scores, find x for both using the formula above, then go from there.
I hope this will help get you started.