How to generate random numbers from different intervals that add up to a fixed sum in excel?

I need to generate 13 numbers from 13 different intervals which will add up to 1345. In the chart below, "index" means the index of the 13 different numbers. Mean means the mean (average) of the intervals. The range will be plus or minus 15% of the mean as shown below. I will prefer to have the random numbers generated based on the normal distribution with N(mean, 7.5% of mean).

It will be great if anyone could figure out how to do it in excel. Algorithms will be appreciated as well.

Index   mean    15% low high
A   288 43  245 331
B   50  8   43  58
C   338 51  287 389
D   50  8   43  58
E   16  2   14  18
F   66  10  56  76
G   118 18  100 136
H   17  3   14  20
I   91  14  77  105
J   26  4   22  30
K   117 18  99  135
L   165 25  140 190
M   18  3   15  21