wha A series of calibration tests is conducted on a pressure

A series of calibration tests is conducted on a pressure gage. At a known pressure of 1000 psia it is found that 30 percent of the readings are within 1 psia of the true value. At a known pressure of 500 psia. 40 percent of the readings are within 1 psia. At a pressure of 200 psia. 45 percent of the readings are within 1 psia. What conclusions do you draw from these readings? Can you estimate a standard deviation for the pressure gage?

Solution

As the pressure is decreasing from 1000psia to 500psia to 200psia the corresponding percentage of readings within 1% of true psia value keeps on increasing. This only means that as the pressure is decreased from 1000 psia to 200psia we are advancing towards the centre(median) of the distribution of readings.

At a pressure of 200psia 45% of reading are within 1 psia. Also from normal distribution we know that the region between 0.6time standard deviation gives the 45% probability. Thus 0.6sd = 1psia

Or sd = 1.67psia.

Thus the standard deviation should be closer to 1.67psia.