Question

If X is a normal variable with mean 100 and standard deviation 15, then find the percentage of observations

(i) Having valne more than 85.

(ii) Having value less than 130.

Answer 1

Here, µ = 100; σ = 15

Now,

P[z ≥ – 1] = P[-1 ≤ z ≤ 0] + P[0 ≤ z ≤ ∞]
= P[0 ≤ Z ≤ 1] + 0.5000
= 0.3413 + 0.5000 = 0.8413

Hence, the value of 0.8413 × 100 = 84.13 % observations is more than 85.

Now,

P[z ≤ 2] = P[- ∞ < Z ≤ 0] + P[0 ≤ z ≤ 2]
= 0.5000 + 0.4772 = 0.9772

Hence, the value of 0.9772 × 100 = 97.72 % observations is less than 130.