Resultant of two distribution (Normal)

If there are two normal distribution having mean and s.d M1,SD1 and M2,SD2 respectively, what would be the mean and s.d of the resultant these two distribution. I usderstand that the resultant of these two will also be a normal distribution.

For example, the particle size distribution in two containers are (M1, SD1) and (M2,SD2) and both are mixing to a third container, what would be the mean, standard deviation of the mixer in third container.

Similarly, if two systems are in series, how can I find the resultant of these two distribution. For ex, there are two crushing mill, both have a crushing size distribution. From first crusher material goes to second one. How can I find the distribution of final output.



your answer is dependent to type of function that it is between two normal variables
what is your intent ?
please speak clearly
is your function y=x1+x2 that x1 and x2 are normal variables and y is Resultant of two normal variables or another things
but the first you say about type of two normal function Resultant then
we could speak about its sd and mean
Dear Elnaz,

Thanks for your reply and sorry if I couldn't explain my problem properly. I would like to request you to have a look at the attachment (diagram.pdf). It is a problem I am facing in real life. Say, there are two containers having some samples of quality following a normal distribution having mean & std dev M1, SD1 & M2, SD2 respectively. This two samples are mixing in a third container. The quality of the mixed samples must follow a normal distribution. How to find out the mean & std dev of the quality of the mixed sample?

In second case, the two system are in series, what would be the mean & std dev of the quality of the mixed sample?

Hope I can explain the my requirement.


TS Contributor
Unfortunately this is not a straightforward calculation....

In the upper part of your diagram, there is no guarantee that the mixed distribution will be normally distributed. An extreme example to make my point: what if you mixed a container of sand (small particles) with a container of marbles (large particles)? The resultant distribution will be bi-modal (two "humps" separated by a large amount). The mean will simply be the weighted mean of the two original means. I don't know if there is a general formula to determine the mixed standard deviation.

In the second situation, I believe the resultant mean will be the product of the first two means, but I'm not 100% positive about that.
Thanks JohnM for you views. But in real life, people must be used some logics to get the result. Because I have seen peoples to use it in a vriety of form in Market Research field. If you can fine some sorts of solutions please let me know.