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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 height
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
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2021-08-14T20:22:59+00:00
2021-08-14T20:22:59+00:00 1 Answers
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Answer:
1.56
Step-by-step 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