Question

2. A population of workers in Italy has income I distributed as a normal distribution with parameters µ = 30,500, σ² = 16, 000.

Suppose everybody is subjected to a tax rate of 25% on their earned income. What is the expected tax revenue from a randomly selected worker?

Answer 1

Solution :

Given that,  

mean = $\mu$ = 30500

Population variance = σ^{2 =} 16, 000.

standard deviation = $\sigma$ = 126.49

Using standard normal table ,

P(Z < z) = 25%

P(Z < z) = 0.25

P(Z < -0.67) = 0.25

z = -0.67

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = -0.67 * 126.49 + 30500 = 30415.25

The expected tax revenue from a randomly selected worker is 30415.25