Experiment of the Month  Statistics of Marble Scattering   In
the marble scattering laboratory, students measured the mean
diameter of a population of marbles by scattering "shooter"
marbles from target marbles. They used a statistical result for
the unce rtainty in their answer, which is derived here. The
result is that the fractional uncertainty in the answer, for N
repeated measurements is notation. In the typical experiment,
each group rolls 25 shooter marbles and counts the number of
times that the shooter hits one of the target marbles. From this
number of hits, they calculate a value, x, for the marble
diameter. They repeat this experiment N ti mes, calculating a
marble diameter each time. Then the group calculates a mean
diameter for their marbles, averaging over all N of their
calculated marble diameters.  10 other groups do the same thing.
To estimate the uncertainty in a single groups mean value for
the diameter, we ask, "If the experiment is repeated, what is
the range of diameters that we might e