1. **State the problem:** Calculate the Human Development Index (HDI) given the Life Expectancy Index (LE) = 85, Mean School Years Index (MSYI) = 0.91, and Expected School Years Index (ESYI) = 0.94. 2. **Formula:** The HDI is calculated as the geometric mean of three indices: Life Expectancy Index (LEI), Education Index (EI), and Income Index (II). Here, Education Index (EI) is the average of MSYI and ESYI. $$\text{HDI} = \sqrt[3]{LEI \times EI \times II}$$ Since Income Index (II) is not provided, we assume HDI is approximated by the geometric mean of LEI and EI only for this problem. 3. **Calculate Education Index (EI):** $$EI = \frac{MSYI + ESYI}{2} = \frac{0.91 + 0.94}{2} = 0.925$$ 4. **Calculate HDI:** $$HDI = \sqrt[3]{LEI \times EI \times II}$$ Assuming Income Index (II) = 1 (since not given), $$HDI = \sqrt[3]{85 \times 0.925 \times 1}$$ But LEI should be normalized between 0 and 1. Since LE = 85 years, we normalize it by dividing by a maximum expected life expectancy, usually 85 years: $$LEI = \frac{85}{85} = 1$$ So, $$HDI = \sqrt[3]{1 \times 0.925 \times 1} = \sqrt[3]{0.925}$$ 5. **Calculate cube root:** $$HDI = 0.975$$ 6. **Round off to two decimal places:** $$HDI = 0.98$$ **Final answer:** \boxed{0.98}