Question: 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 = 0.08 milligram (mg) because the weighing is not perfectly precise. The dust on a particular filter actually weight 123 mg. Repeated weighing will then have the Normal distribution with the mean 123 mg and standard deviation 0.08 mg.

a. The laboratory reports the mean of 3 weighing. What is the distribution of this mean?

b. What is the probability that the laboratory reports a weight of 124 mg or higher for this filter?