An engine wear test is to be carried out in which the weight of radioactive piston ring particles in an oil sample is to be determined. A sample of the used oil gives 15,734 counts over a 3-min period. A standard has been prepared using exactly 100 μg of the same activity material which gives 82,396 counts over a 10-min period. Background for the detector has been determined to be 281 counts/min, measured over a very long counting period (~24 h). Find the weight of the particles in the sample and its expected fractional standard deviation.