generate normally distributed variables that sum to a constant value

I am trying to generate random layer thicknesses that sum to a constant total. For example, The total deposit thickness is 10 meters. Layer 1 is on average 29% of the total with a standard deviation of 16%. Layer 2 Avg 51% stdev 18%. Layer 3 Avg 20% stdev 20%. Thanks for the help.

Answer 1

[Walter Roberson]

You might be be able to adapt http://www.mathworks.com/matlabcentral/fileexchange/9700-random-vectors-with-fixed-sum