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There is every reason to expect your data to fit a binomial
distribution since it is the correct distribution. However, as Mr.
Cleyet correctly points out, the Poisson distribution is more useful
here because of the huge number of nuclei in your sample (on the order
of 10^23) and the virtually zero probability that any one nucleus will
decay during the counting interval.
//// As you can see#counts #times c*t c! P(k;mu(c)) Expected #times = %diff =
in the table below, your data with a 0.5 second counting interval fits
a Poisson distribution very well. I leave it to you and your students
to analyze your data with a Gaussian distribution.
A final note. Remember to keep in mind that your measured count rate
is not the same thing as the decay rate of your sample.....
Glenn A. Carlson, P.E.