If you make independent trials with the same random variable , which has expected value and standard deviation , you can then sum the random variables. That sum will be approximately normally distributed when is sufficiently large.
Rule
has expected value
and standard deviation
Example 1
You let be a randomly selected cheese at the cheese counter. The expected value of the weight of such a cheese is , with a standard deviation of . If you let denote the sum of 50 such cheeses, what is the expectation value and the standard deviation for ?
You know that
You also know that