1. **State the problem:** We want to find the estimated breeding value (EBV) and the accuracy of the EBV for the average daily growth rate of a pig. Given data: - Population average daily growth rate, $\bar{P} = 875$ grams/day - Common environmental effect for full-sibs, $c^2 = 0.5$ - Average daily growth rate of 10 full-sibs, $\bar{F} = 675$ grams/day - Heritability for slaughter weight, $h^2 = 0.45$ 2. **Calculate the EBV:** The EBV can be estimated using the formula: $$\text{EBV} = h^2 \times (\bar{F} - \bar{P})$$ Calculate the difference: $$\bar{F} - \bar{P} = 675 - 875 = -200$$ Then, $$\text{EBV} = 0.45 \times (-200) = -90$$ So, the estimated breeding value is $-90$ grams/day. 3. **Calculate the accuracy of the EBV:** Accuracy ($r$) is given by: $$r = \sqrt{\frac{n h^2}{1 + (n - 1) c^2}}$$ where $n$ is the number of full-sibs (10). Calculate the denominator: $$1 + (10 - 1) \times 0.5 = 1 + 9 \times 0.5 = 1 + 4.5 = 5.5$$ Calculate the numerator: $$10 \times 0.45 = 4.5$$ Therefore, $$r = \sqrt{\frac{4.5}{5.5}} = \sqrt{0.8182} \approx 0.9045$$ 4. **Final answers:** - Estimated Breeding Value (EBV) = $-90$ grams/day - Accuracy of EBV estimate = $0.90$