(Solved): Suppose that we will take a random sample of size \( n \) from a population having mean \( \mu \) a ...

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 \( \bar{x} \) : (a) \( \mu=16, \sigma=2, n=48 \) (Round your answers of " \( a \quad \) " and " \( a \quad 2 n \) to 4 decimal places.) (b) \( \mu=513, \sigma=6, n=140 \) (Round your answers of " \( \sigma \quad \) " and " \( \sigma \quad 2 \) n to 4 decimal places.) (c) \( \mu=6, \sigma=10, n=9 \) (Round your answers of " \( \sigma \), " and " \( \sigma \quad 2= \) to 4 decimal places.) (d) \( \mu=104, \sigma=2, n=1,345 \) (Round your answers of " \( a \quad \) " and " \( a \quad 2 . \) to 4 decimal places.)