1. **State the problem:** We are given a population mean $\mu = 550$ and population standard deviation $\sigma = 75$. We want to find the mean and variance of the sample means for a sample size $n=50$. 2. **Recall the formulas:** - The mean of the sample means $\mu_x$ is equal to the population mean: $$\mu_x = \mu$$ - The variance of the sample means $\sigma_x^2$ is the population variance divided by the sample size: $$\sigma_x^2 = \frac{\sigma^2}{n}$$ 3. **Calculate the population variance:** $$\sigma^2 = 75^2 = 5625$$ 4. **Calculate the mean of the sample means:** $$\mu_x = 550$$ 5. **Calculate the variance of the sample means:** $$\sigma_x^2 = \frac{5625}{50} = 112.5$$ 6. **Summary:** - Mean of sample means $\mu_x = 550$ - Variance of sample means $\sigma_x^2 = 112.5$ These values are rounded to two decimal places as requested.