1. **Stating the problem:** We are given a probability distribution for the number of houses sold (x) and their probabilities P(x). We need to find the mean (expected value) $\mu$ of the distribution. 2. **Formula for mean:** The mean of a discrete probability distribution is given by: $$\mu = \sum x \cdot P(x)$$ This means we multiply each value of $x$ by its probability $P(x)$ and then sum all these products. 3. **Given data:** \[ \begin{array}{c|c} x & P(x) \\\hline 0 & 0.24 \\ 1 & 0.01 \\ 2 & 0.12 \\ 3 & 0.16 \\ 4 & 0.01 \\ 5 & 0.14 \\ 6 & 0.11 \\ 7 & 0.21 \\ \end{array} \] 4. **Calculate each product:** $$0 \times 0.24 = 0$$ $$1 \times 0.01 = 0.01$$ $$2 \times 0.12 = 0.24$$ $$3 \times 0.16 = 0.48$$ $$4 \times 0.01 = 0.04$$ $$5 \times 0.14 = 0.70$$ $$6 \times 0.11 = 0.66$$ $$7 \times 0.21 = 1.47$$ 5. **Sum all products to find mean:** $$\mu = 0 + 0.01 + 0.24 + 0.48 + 0.04 + 0.70 + 0.66 + 1.47$$ $$\mu = 3.60$$ 6. **Interpretation:** The mean number of houses sold is 3.60. **Final answer:** $\boxed{3.60}$ which corresponds to option A.