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 greater than 72 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(Greater than 72 inches)

P = P(X > 72)

When x = 72

z = `(72 - 68)/3 = 4/3` = 1.33

P(x > 72) = P(z > 1.33)

= 0.5 – 0.4082

= 0.0918

Number of students whose height are greater than 72 inches

= 0.0918 × 500

= 45.9

= 46  ......(approximately)