(Solved): Suppose that XN(500,100). You're considering taking a simple random sample and calculating the a ...

Suppose that $X?\mathrm{N}(500,100)$. You're considering taking a simple random sample and calculating the average of your sample. The Central Limit Theorem tells us that the distribution of all possible sample averages is Normally distributed with a mean of 500. What is its standard deviation, if you took a sample of size $n=100$ ?