1. **Stating the problem:** We are given a sample mean $\bar{x} = 3$ with frequency 1 and probability $\frac{1}{25}$. We need to compute the mean of the sampling distribution $\mu_x$ and the variance and standard error. 2. **Formula for mean of sampling distribution:** $$\mu_x = \sum \bar{x} \cdot P(X=\bar{x})$$ 3. **Calculate mean of sampling distribution:** Given only one sample mean 3 with probability $\frac{1}{25}$, $$\mu_x = 3 \times \frac{1}{25} = \frac{3}{25}$$ 4. **Formula for variance of sampling distribution:** $$\sigma_x^2 = \sum P(X=\bar{x}) \cdot (\bar{x} - \mu_x)^2$$ 5. **Calculate $(\bar{x} - \mu_x)^2$:** $$\left(3 - \frac{3}{25}\right)^2 = \left(\frac{75}{25} - \frac{3}{25}\right)^2 = \left(\frac{72}{25}\right)^2 = \frac{5184}{625}$$ 6. **Calculate variance:** $$\sigma_x^2 = \frac{1}{25} \times \frac{5184}{625} = \frac{5184}{15625}$$ 7. **Calculate standard error (standard deviation):** $$\sigma_x = \sqrt{\frac{5184}{15625}} = \frac{72}{125} = 0.576$$ **Final answers:** - Mean of sampling distribution $\mu_x = \frac{3}{25} = 0.12$ - Variance $\sigma_x^2 = \frac{5184}{15625} \approx 0.3318$ - Standard error $\sigma_x = 0.576$