Question

The annual salaries of employees in a large company are approximately normally distributed with a mean of $50,000 and a standard deviation of $20,000. What percent of people earn less than $40,000?

Answer 1

Let x denotes the annual salaries of employees in a large company

Mean µ = 50,000 and S.D σ = 20,000

P(people earn less than $40,000) = P(X < 40,000)

When x = 40,000

z = `(40, 000 - 50, 000)/(20 000)`

= `(10,000)/(20,000)`

z = – 0.5

P(X < 40,000) = P(Z < – 0.5)

= P(`-oo` < z < 0) – P(– 0.5 < z < 0)

= 0.5 – P(– 0.5 < z <0)

= 0.5 – P(0 < z < 0.5)  ......(Due to symmetry)

= 0.5 – 0.01915

= 0.3085

= P(X < 40,000) in percentage

= 0.3085 × 100

= 30.85