Statistics Problem/Question

I am not looking for an exact answer for the following question, but
rather for an approximate answer.

Say you had 30 low-mass red dwarfs (unbiased sample) whose masses are
all measured to +/- 0.01 solar mass. Say you added all 30 masses and
divided by 0.145 solar mass.

What would the approximate (or exact if you prefer) probability be for
find ing an exact multiple? What would be the expected probability for a
deviation of +/- 0.001 solar mass, and finally what would be the
expected probability for a deviation of +/- 0.01 solar mass?

What I am looking for is a better feeling for whether it makes sense to
do such a test and whether a result that comes from such a test might be
meaningful or misleading.=20

First, second, third, fourth, ... opinions are most welcome.