Question: Suppose that we will take a random sample of size \(n\) from a population having mean \(\mu\) and standard deviation \(\sigma\). For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean \(\bar{x}\) :

1. \(\mu=10, \quad \sigma=2, \quad n=25\)
2. \(\mu=500, \quad \sigma=.5, \quad n=100\)
3. \(\mu=3, \quad \sigma=.1, \quad n=4\)
4. \(\quad \mu=100, \quad \sigma=1, \quad n=1,600\)

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