Question

The random variable X is normally distributed with mean of 80 and variance of 36. The 67th percentile of the distribution is

Answer 1

82.64

Explanation:

Mean = 80 ; σ² = 36 ; σ = √36 = 6

Using the relation :

P(Z < x) = (x - mean) / standard deviation

P(Z < x) = 0.67

Z = invNorm(0.67) = 0.44

Hence,

0.44 = (x - 80) / 6

Cross multiply :

6 * 0.44 = x - 80

2.64 = x - 80

2.64 + 80 = x

82.64 = x

Hence, X = 82.64