The Mean, Standard Deviation, and Sampling Distribution of the Sample Mean

1. Random samples of size $225$ are drawn from a population with mean $100$ and standard deviation $20$. Find the mean and standard deviation of the sample mean.

3. A population has mean $75$ and standard deviation $12$.

1. Random samples of size $121$ are taken. Find the mean and standard deviation of the sample mean.
2. How would the answers to part (a) change if the size of the samples were $400$ instead of $121$?