# Statistics for sum of elements of a sample

I'm looking to find an expected mean and standard deviation from summing across the elements of a sample from a normal distribution.

Say we have a normally distributed population with mean of 1000 and standard deviation of 10, of which I am taking a sample of 100.

Intuition tells me that my expected value would be n*μ = 100 * 1000 = 100000; but I'm not sure how to construct any statistic for expected variance around that value.