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 between 65 and 71 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(Between 65 and 71 inches)

P(65 ≤ x ≤ 71)

When x = 65

z = `(65 - 68)/3 = (-3)/3 = - 1`

When x = 71

z = `(71 - 68)/3 = 3/3` = 1

P(65 ≤ x ≤ 71) = P(– 1 < z < 1)

= P(– 1 < z < 0) + P(0 < z < 1)

= P(0 < z < 1) + P(0 < z < 1)

= 2 × [P(0 < z < 1)]

= 2 × 0.3413

= 0.6826

∴ Number of students whose height between 65 and 7 inches

= 0.6826 × 500

= 341.3

= 342  .......(approximately)