5. A laboratory weights filters from a coal mine to measure the amount of dust in the mine atmosphere. Repeated measurements of the weight of dust on the same filter has a standard deviation of σ = 0.08 milligram (mg) and mean 123 mg.

(a) If 3 weightings of this filter are made what is the distribution of this mean? What can be said about the mean and standard deviation of this distribution?

(b) If 32 weightings of this filter are made what is the distribution of this mean? What can be said about the mean and standard deviation of this distribution?