Question

Exercise 4. Male height is normally distributed with mean 70 (a) Jim is 67 inches tall. What is the z-score for his height? What (b) Joe is 76 inches tall. What is the s-score for his height? What (c) What proportion of men are shorter than Joe, but taller than inches, and σ 3 inches. proportion of men are shorter and taller than Jim? proportion of men are shorter and taller than Joe Jim?

Answer 1

μ = 70, σ = 3

(a) x = 67

z = (x - μ)/σ = (67 - 70)/3 = -1

P(x < 67) = P(z < -1) = 0.1587

P(x > 67) = P(z > -1) = 0.8413

(b) x = 76

z = (x - μ)/σ = (76 - 70)/3 = 2

P(x < 76) = P(z < 2) = 0.9772

P(x > 76) = P(z > 2) = 0.0228

(c) P(67 < x < 76) = P(-1 < z < 2) = 0.8186