1. **State the problem:** Calculate the Human Development Index (HDI) given the Life Expectancy Index (LE) = 85, Mean School Years Index (MSYI) = 91, and Expected School Years Index (ESYI) = 0.94. 2. **Formula:** The HDI is calculated as the geometric mean of the three indices: $$\text{HDI} = \sqrt[3]{LE \times MSYI \times ESYI}$$ 3. **Important notes:** - Each index should be normalized between 0 and 1 before calculation. Since LE and MSYI are given as percentages or values out of 100, we convert them to decimals. - LE = 85 means 0.85, MSYI = 91 means 0.91, ESYI is already 0.94. 4. **Calculate:** $$\text{HDI} = \sqrt[3]{0.85 \times 0.91 \times 0.94}$$ Calculate the product inside the root: $$0.85 \times 0.91 = 0.7735$$ $$0.7735 \times 0.94 = 0.72649$$ 5. **Find the cube root:** $$\text{HDI} = \sqrt[3]{0.72649}$$ Using a calculator: $$\text{HDI} \approx 0.90$$ 6. **Final answer:** The Human Development Index (HDI) is approximately **0.90** (rounded to two decimal places). \boxed{0.90}