5.85 Dust in coal mines. A laboratory weighs 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 vary Normally with standard deviation σ = 0.09 milligram (mg) because the weighing is not perfectly precise. The dust on a particular filter actually weighs 137 mg.
(a) The laboratory reports the mean of three weighings of this filter. What is the distribution of this mean?
(b) What is the probability that the laboratory reports a weight of 140 mg or higher for this filter?