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Interpret the Data Given - Women in the Army

Given the information below (and attached), please determine: Are women being denied the opportunity to join the Army because they are too short or too tall?

If the required women's height for the Army is between 58 and 80 inches.

The Mean = 63.3, and the SD = 2.5

What percentage of women meet that height requirement?

First plug in the low end of that requirement: Z = (58 - 63.6) / 2.5 = -2.24

Now we find the corresponding area under that z value. -2.24 = 0.0125

Now plug in the high value for the requirement: z = (80 - 63.6) / 2.5 = 6.56

We find the corresponding area for that z value: 6.56 = 0.9999

To find the percentage of women between 58 and 80 inches, remember percentage equates with area which is a total of 1. We want to find the total area within the two areas we just calculated. How would we do that?

Percentage of women between the 58 and 80 inch requirement = 0.9999 - 0.0125 = .9874 or 98.74%

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Solution Summary

Given the information below (and attached), this solution answers the question: Are women being denied the opportunity to join the Army because they are too short or too tall?

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