Question

The average height of a male ROTC cadet is 70 in. Suppose that 10 percent of the male cadets are taller than 72 in. Assuming that the heights of the cadets are normally distributed, what is the standard deviation

Answer 1

1.56

Explanation:

Given that :

Average height (μ) = 70 in

10% are taller than 72 in ; the standard deviation Given a normal distribution :

P(x > Z) = 0.10

Using a Z probability calculator, the Z value corresponding to P(x > Z) = 0.10 is 1.282

Z = 1.282

Using the Z relation:

Z = (x - μ) / σ

σ = standard deviation x = 72

1.282 = (72 - 70) / σ

1.282σ = 2

σ = 2 / 1.282

σ = 1.5600624

σ = 1.56