The figures are invented. In Country Z the five income quintiles, from poorest to richest, receive 4%, 9%, 15%, 24% and 48% of national income. A worker in Country Z earns $50,000 a year. Income up to $10,000 is not taxed, income from $10,001 to $40,000 is taxed at 20% and income above $40,000 is taxed at 35%. (i) Calculate the cumulative income share of each quintile. [2] (ii) Write down the coordinates of the points that would be plotted to construct the Lorenz curve. [1] (iii) Calculate the income tax the worker pays. [2] (iv) Calculate the worker's average tax rate. [1]

HL Paper 3-style calculation (standalone practice; not an IB question).