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

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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 $12$ .

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