# Generating and summing 100,000 random numbers off a distribution curve

I need to generate a high volume of random numbers off a normal distribution curve and sum them.

I use Excel and am aware of the NormInv(Rand(), Mean, SD) method of generating a random number off a curve. I need a way to do it 100,000 plus times - summing all the results together.

Is there a better statistical way I can arrive at the result without having to run the same calc endless times?

• If I needed more than a couple of thousand numbers I wouldn't use Excel. There are some faster ways to get numbers, but 100000 of them in Excel will still take ages. Of course if you only need to sample from the distribution of the sum (and not do anything else with the numbers) then you don't need to generate more than one number. Feb 19, 2017 at 1:28

The sum of $N$ numbers (such as $N=100,000$) drawn independently from a Normal distribution with mean $\mu$ and standard deviation $\sigma$ has a Normal distribution with mean $N\mu$ and standard deviation $\sigma\sqrt{N}$. Therefore you need merely draw one number from this distribution.

• Sorry. Can you explain in a little more detail. Perhaps even how to do in excel? Pls.
– LILI
Feb 18, 2017 at 20:46
• You already described how to do this in Excel! Just multiply Mean by 100,000 and SD by the square root of 100,000 and generate a single number.
– whuber
Feb 18, 2017 at 20:49
• +1 but hmmm... this is an unusually short answer for you (you tend to post such "trivial" answers as comments) and coincides with you suddenly changing your nickname (slightly but conspicuously) - I hope your account was not hacked! Feb 18, 2017 at 20:50
• @amoeba Sometimes a short answer does everything, especially because in this case the OP has already exhibited the software solution. What is unusual is that I typically elect not to answer questions that have short simple answers: that is a policy designed to give newcomers and people at earlier stages of their statistical education a greater chance to participate.
– whuber
Feb 18, 2017 at 20:54
• Thanks. And that gets me the same as the sum of 100k random nu.ber
– LILI
Feb 18, 2017 at 20:58