1. **State the problem:** We are given probabilities and returns for shares and asked to find the standard deviation of the share returns given the expected return is 23.25%. 2. **List the data:** - Probabilities: $p = [0.15, 0.2, 0.3, 0.25, 0.1]$ - Returns: $r = [0.05, 0.20, 0.40, 0.20, 0.15]$ - Expected return: $E(R) = 0.2325$ 3. **Recall the formula for variance:** $$\sigma^2 = \sum p_i (r_i - E(R))^2$$ 4. **Calculate each squared deviation:** - $(0.05 - 0.2325)^2 = 0.03330625$ - $(0.20 - 0.2325)^2 = 0.00105625$ - $(0.40 - 0.2325)^2 = 0.02830625$ - $(0.20 - 0.2325)^2 = 0.00105625$ - $(0.15 - 0.2325)^2 = 0.00680625$ 5. **Multiply each squared deviation by its probability:** - $0.15 \times 0.03330625 = 0.00499594$ - $0.2 \times 0.00105625 = 0.00021125$ - $0.3 \times 0.02830625 = 0.00849188$ - $0.25 \times 0.00105625 = 0.00026406$ - $0.1 \times 0.00680625 = 0.00068063$ 6. **Sum these values to get variance:** $$\sigma^2 = 0.00499594 + 0.00021125 + 0.00849188 + 0.00026406 + 0.00068063 = 0.01464376$$ 7. **Calculate standard deviation:** $$\sigma = \sqrt{0.01464376} = 0.121\approx 12.1\%$$ 8. **Compare with given options:** The closest option is 12.02%. **Final answer:** The standard deviation of the share returns is approximately **12.02%**.