A laboratory weighs filters from a coal mine to measure the

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 weighs 123 mg. The laboratory reports the mean of 3 weighings of this filter. What is the probability that the laboratory reports a weight of 124 mg or higher for this filter? (Give your answer to the nearest whole number)

Solution

Let X be the weight of dust on the same filter.

X is N(123, 0.08)

x bar is normal with N(123, 0.08/rt 3)

= (123, 0.0462)

P(X>=124) =P(Z>=1/0.0462)

= P(Z>21.65)

=0.00