Suppose a population has a mean of $3200$ and a standard deviation of $8$. If random samples of size $1600$ are selected, what are the mean and standard deviation of the sampling distribution of the sample means?

• A. ${\mu }_{\bar{x}}=1600.0$${\sigma }_{\bar{x}}=8.0$
• B. ${\mu }_{\bar{x}}=3200.0$${\sigma }_{\bar{x}}=8.0$
• C. ${\mu }_{\bar{x}}=1600.0$${\sigma }_{\bar{x}}=0.2$
• D. ${\mu }_{\bar{x}}=3200.0$${\sigma }_{\bar{x}}=0.2$

Answer: (D)