Answer:
93.03%
Step-by-step explanation:
Population mean (μ) = 66.1 inches
Standard deviation (σ) = 2.7 inches
The z-score for a given 'X' value is:
[tex]z = \frac{X- \mu}{\sigma}[/tex]
For X = 62 inches
[tex]z = \frac{62- 66.1}{2.7}\\z=-1.5185[/tex]
A z-score of -1.5185 corresponds to the 6.44-th percentile of a normal distribution.
For X = 62 inches
[tex]z = \frac{73- 66.1}{2.7}\\z=2.5555[/tex]
A z-score of 2.5555 corresponds to the 99.47-th percentile of a normal distribution.
The total percentage of men eligible for the military is the percentage within those two values, therefore:
[tex]E = 99.47-6.44\\E=93.03 \%[/tex]
93.03% this country's men are eligible for the military based on height.
