Question

1. The salaries of the employees in a company follow the normal distribution with mean $16000 and standard deviation $800.

(a) What is the probability that the salary of an employee is higher than $18000? (3 marks)
(b) There is 80% chance that the salary of an employee is less than $t. Find the value of t.

Answer 1

Let X will be the random variable denotes the salaries of the employees.

Mean μ = 16000

Standard deviation σ = 800

X ~ N(μ = 16000, σ = 800)

$Z = \frac{X – μ}{σ} = \frac{X – 16000}{800} \\ (a) \; P(X > 18000) = P(\frac{X – μ}{σ} > \frac{18000 – 16000}{800} )\\ = P(Z > 2.5) \\ = 1 – P(Z <= 2.5) \\ = 1 – 0.9937 \\ = 0.0062 \\ (b) \; P(X < t) = 0.80 \\ P(\frac{X – μ}{σ} < \frac{t – 16000}{800}) = 0.80 \\ P(Z < \frac{t – 16000}{800}) = 0.80 \\ \frac{t – 16000}{800} = 0.8416 \\ t = 16000 + 800 \times 0.8416 \\ t = 16673.28$