Heights of adult American males are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches.

Heights of adult American males are normally distributed with a mean of 69.0 inches and a standard deviation of 2.8 inches. The U.S. Marine Corps requires that males have heights between 64 inches and 78 inches. What percentage of males are eligible for the Marines based on height?

Expert Solution

µ = 69 , σ = 2.8

P(64 < x < 78)

Percentage of male which is required:

= P(64 – 69/2.8 < z < 78 – 69/2.8) [a = x-µ/σ]

= P(-1.79 < z < 3.21)

= P(z < 3.21) – P(z < 1.79)

= 0.9993 – 0.0367

= 09626 ≈ 96.26%

Percentage of heights of male = 96.36 %

Junaid answered 2 years ago

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