In a sophisticated medicine research center, two scales are used for repeated weighing of the same item. If the true weight of a compound is 2 grams [g], the first scale produces readings X that have a mean 2.0 g and standard deviation 0.03 g. The second scale’s readings Y have mean 2.001 g and standard deviation 0.01 g.

Question

In a sophisticated medicine research center, two scales are used for repeated weighing of the same item. If the true weight of a compound is 2 grams [g], the first scale produces readings X that have a mean 2.0 g and standard deviation 0.03 g. The second scale’s readings Y have mean 2.001 g and standard deviation 0.01 g. 
a)	Which scale is more appropriate for the measurement? 
b)	What are the mean and standard deviation of the difference Y-X between the readings? (The readings X and Y are independent)    
c)	You measure once with each scale and average your readings. Your result is Z=½(X+Y). What are μZ and σZ? Is the average Z more or less variable than the reading Y of the less variable scale?