A calibration laboratory has been measuring a one-kilogram checkweight by the same procedure for several years. They have accumulated several hundred measurements, and the SD of these measurements is 18 micrograms. Someone now sends in a one-kilogram weight to be calibrated by the same procedure. The lab makes 50 measurements on the new weight, which average 78.1 micrograms above 1 kilogram, and their SD is 20 micrograms. Assume the Gauss model. Required:
a. About how many micrograms is the standard error of one measurement?
b. About how many micrograms is the standard error of the average of 50 measurements?
c. Find a 90%-confidence interval for how many micrograms this new weight is above 1 kilogram.