Question

In a certain country the heights of adult men are normally distributed with a mean of 70.4 inches and a standard deviation of 2.6 inches. The​ country's military requires that men have heights between 66 inches and 77 inches. Determine what percentage of this​ country's men are eligible for the military based on height.

Answer 1

To determine the percentage of men who are eligible for the military based on height, we need to find the proportion of men whose heights are between 66 inches and 77 inches.

First, we can standardize the values of 66 inches and 77 inches using the formula z = (x - μ) / σ, where x is the height, μ is the mean height, and σ is the standard deviation. For x = 66 inches:

z = (66 - 70.4) / 2.6 = -1.6923

And for x = 77 inches:

z = (77 - 70.4) / 2.6 = 2.5

We can then use a standard normal distribution table or calculator to find the area under the curve between these two z-scores:

P(-1.6923 < Z < 2.5)

Using a standard normal distribution table or calculator, we find that this probability is approximately 0.9222.

Therefore, about 92.22% of men in this country are eligible for the military based on height.