Question

If the heights of 500 students are normally distributed with mean 68.0 inches and standard deviation 3.0 inches, how many students have height less than or equal to 64 inches

Answer 1

Let x denote the height of a student N = 500; m = 68.0 inches and σ = 3.0 inches the standard normal variate

z = `(x - mu)/sigma = (x - 68)/3`

P(Less than or equal to 64 inches)

P(X ≤ 64)

When x = 64

z = `(64 - 68)/3 = (-4)/3 = - 1.33`

P(X ≤ 64) = P(Z ≤ – 1.33)

P(Z ≥ – 1.33)

= 0.5 – 0.4082

= 0.0918

∴ Number of heights who ate less than or equal to 64 inches

= 0.0918 × 500

= 45.9

= 46  .......(approximately)