Combining Normal Distributions

Coriorda said:

Hello All,
I have a practical problem that I would appreciate your advice on.

The weights of individual livestock at age X are normally distributed with mean A and standard deviation of B.
Similarly livestock at age X+1, X+2 etc etc also follow a normal distribution with their own mean and Standard deviation.

Normally only one age band is processed at a time. However, if more than 1 age band were to be processed, what would the mean weight and standard deviation of the mixed animals be.? Is it as simple as taking an average of the means and summing the variances?

Many Thanks for any help you can offer.

Rgds
Coriorda

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Ishuda said:

If you mixed two groups, you would have a bimodal distribution. As an extreme example suppose you had one group which had a 700 lb weight average with a standard deviation 20 lbs and another group which had an 800 lb weight average with a standard deviation of 20 lb. If you mixed the groups, there would be a set grouped around 700 lbs and another set grouped around 800 lbs.

The wikipedia page
http://en.wikipedia.org/wiki/Multimodal_distribution
talks about bimodal distributions and shows a specific example of mixing two normal distributions.

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